Are there different types of emptiness (Śūnyatā)?

The answer is No, there are not different types of emptiness.

The historical Buddha taught that we humans are made up of five skandhas, sometimes called the five aggregates or five "heaps." These are form, sensation, perception, mental formation, and consciousness. The Buddha was describing our bodies and the functions of our nervous systems -- sensing, feeling, thinking, recognizing, forming opinions, being aware.

As recorded in the Anatta-lakkhana Sutta of the Pali Tipitaka (Samyutta Nikaya 22:59), the Buddha taught that these five "parts," including our consciousness, are not "self." They are impermanent, and clinging to them as if they were the permanent "me" gives rise to greed and hate, and to the craving that is the source of suffering (see the Four Noble Truths).

The teaching in the Anatta-lakkhana Sutta is called "anatta," sometimes translated "no self" or "not self." This basic teaching is accepted in all schools of Buddhism, including Theravada. Anatta is a refutation of the Hindu belief in atman -- a soul; an immortal essence of self.

But Mahayana Buddhism goes further than Theravada, and teaches that all phenomena are without self-essence. This is sunyata.

Do not misunderstand sunyata to mean that nothing exists. It tells us that there is existence, but that phenomena are empty of svabhava, a Sanskrit word that means self-nature, intrinsic nature, essence, or "own being." And sunyata has no intrinsic nature that one could call a "type".

If I relate emptiness to my own practice, what I first see is there are many types of emptiness, but as I sit quietly with this, I realize it is not emptiness that is multiple, but it is my changing perception that creates the illusion that emptiness is changing. Emptiness is the same, yet my perception of it is never the same. So as many different states of consciousness that are possible, that is how many possible perceptions of emptiness there are. A simple example from nature, an Eskimo sees water as ice, a Fijian sees water as ocean, a person from the Great Lakes sees water as the lakes. They are all observing water, though in different forms. When we wake up, the perceptions appear as they are, but we are not fooled. We know they are all water.

Actually, there are different perspectives on emptiness within Tibetan madhyamaka. One might even say different types of emptiness! On the one hand there is "rangtong" which means "empty of self" and there is shendong, meaning "empty of other". The idea of shendong, "empty of other", implies that dharmakaya or the Buddha nature is not itself empty of intrinsic nature. Shendong might be interpreted to say that emptiness itself is not empty - quite contrary to Nagarjunas exposition, I'd say. For a good discussion on this subject, I reccomend Guy Newland's talks on varieties og Tibetan Madhyamka. You can easily find it on YouTube. The shendong/rangtong difference can be explained in many ways, and different emphasis can be but - especially on the shendong side

Since this answer is based on research and my other answer was based on my experience alone, I am starting another answer in the hope of avoiding confusion with all the previous comments. The following posits that the original approach to sunyata is positive. http://en.wikipedia.org/wiki/Mahayana

According to some scholars, the Buddha nature discussed in some Mahāyāna sūtras does not represent a substantial self (ātman); rather, it is a positive language and expression of emptiness (śūnyatā) and represents the potentiality to realize Buddhahood through Buddhist practices.[51] It is the "true self" in representing the innate aspect of the individual that makes actualizing the ultimate personality possible.

Prior to this Mahayana held a different definition of emptiness

Prior to the period of these sūtras, Mahāyāna metaphysics was dominated by teachings on emptiness, in the form of Madhyamaka philosophy. The language used by this approach is primarily negative, and the Buddha nature genre of sūtras can be seen as an attempt to state orthodox Buddhist teachings of dependent origination and on the mysterious reality of nirvana using positive language instead, to prevent people from being turned away from Buddhism by a false impression of nihilism. In these sūtras the perfection of the wisdom of not-self is stated to be the true self; the ultimate goal of the path is then characterized using a range of positive language that had been used in Indian philosophy previously by essentialist philosophers, but was now transmuted into a new Buddhist vocabulary that described a being who has successfully completed the Buddhist path.[52]

There is one more citation that speaks to the subtle differences of the different schools in relation to emptiness. http://en.wikipedia.org/wiki/Buddhism

Emptiness Main article: Śūnyatā Mahayana Buddhism received significant theoretical grounding from Nagarjuna (perhaps c. 150–250 CE), arguably the most influential scholar within the Mahayana tradition. Nagarjuna's primary contribution to Buddhist philosophy was the systematic exposition of the concept of śūnyatā, or "emptiness", widely attested in the Prajñāpāramitā sutras that emerged in his era. The concept of emptiness brings together other key Buddhist doctrines, particularly anatta and dependent origination, to refute the metaphysics of Sarvastivada and Sautrantika (extinct non-Mahayana schools). For Nagarjuna, it is not merely sentient beings that are empty of ātman; all phenomena (dharmas) are without any svabhava (literally "own-nature" or "self-nature"), and thus without any underlying essence; they are "empty" of being independent; thus the heterodox theories of svabhava circulating at the time were refuted on the basis of the doctrines of early Buddhism. Nagarjuna's school of thought is known as the Mādhyamaka. Some of the writings attributed to Nagarjuna made explicit references to Mahayana texts, but his philosophy was argued within the parameters set out by the agamas. He may have arrived at his positions from a desire to achieve a consistent exegesis of the Buddha's doctrine as recorded in the Canon. In the eyes of Nagarjuna the Buddha was not merely a forerunner, but the very founder of the Mādhyamaka system.[56]

Sarvastivada teachings—which were criticized by Nāgārjuna—were reformulated by scholars such as Vasubandhu and Asanga and were adapted into the Yogacara (Sanskrit: yoga practice) school. While the Mādhyamaka school held that asserting the existence or non-existence of any ultimately real thing was inappropriate, some exponents of Yogacara asserted that the mind and only the mind is ultimately real (a doctrine known as cittamatra). Not all Yogacarins asserted that mind was truly existent; Vasubandhu and Asanga in particular did not.[57] These two schools of thought, in opposition or synthesis, form the basis of subsequent Mahayana metaphysics in the Indo-Tibetan tradition.

Besides emptiness, Mahayana schools often place emphasis on the notions of perfected spiritual insight (prajñāpāramitā) and Buddha-nature (tathāgatagarbha). There are conflicting interpretations of the tathāgatagarbha in Mahāyāna thought. The idea may be traced to Abhidharma, and ultimately to statements of the Buddha in the Nikāyas. In Tibetan Buddhism, according to the Sakya school, tathāgatagarbha is the inseparability of the clarity and emptiness of one's mind. In Nyingma, tathāgatagarbha also generally refers to inseparability of the clarity and emptiness of one's mind. According to the Gelug school, it is the potential for sentient beings to awaken since they are empty (i.e. dependently originated). According to the Jonang school, it refers to the innate qualities of the mind that expresses themselves as omniscience etc. when adventitious obscurations are removed. The "Tathāgatagarbha Sutras" are a collection of Mahayana sutras that present a unique model of Buddha-nature. Even though this collection was generally ignored in India,[58] East Asian Buddhism provides some significance to these texts.

It appears that there are different interpetations of what emptiness is based on the basic precepts that a Buddhist sect adheres to.

Or then we can just stick to the simplicity of what the Buddha says to Ananda"

http://en.wikipedia.org/wiki/%C5%9A%C5%ABnyat%C4%81

Pali Canon[edit]

A simile from the Pali scriptures (SN 22.95) compares form and feelings with foam and bubbles. The Pali canon uses the term emptiness in three ways: "(1) as a meditative dwelling, (2) as an attribute of objects, and (3) as a type of awareness-release." [7] The Suñña Sutta,[8] part of the Pāli canon, relates that the monk Ānanda, Buddha's attendant asked,

It is said that the world is empty, the world is empty, lord. In what respect is it said that the world is empty?" The Buddha replied, "Insofar as it is empty of a self or of anything pertaining to a self: Thus it is said, Ānanda, that the world is empty.