What is the difference between Anapanasati and Vipassana?

Anapana is a pali term, the in-&-out breaths are spoken of in that way. As to Kayagatasati, mindfulness of the body is spoken of in that way. Anapana are bodily fabrications, the breathing is a thing tied to the body. When one anapanasati one is doing kayagatasati, one classification is included in the other classification.

The difference is that Anapanasati is particularly effective at cutting off distracting thoughts and the breaths are wind element whereas the bodily sensations are generally earth element.

Vipassana as it is taught by ie Yuttadhamma Bhikkhu, is in short, a bit of both.

I have not yet read the Pali suttas refer to "vipassana" alone as the direct path to Nibbana. At least SN 43.2 says:

Katamo ca, bhikkhave, asaṅkhatagāmimaggo?

And what is the path that leads to the unconditioned?

Samatho ca vipassanā ca

Tranquility and insight

The term "anapanasati" is used in a very specific manner in the Pali suttas to refer to a combined fruition over 16 stages of concentration, tranquility & insight; where tranquility has increasing significance the earlier the stage and where vipassana has increasing significance the later the stage. Refer to MN 118 for a complete explanation.

The term "vipassana" ("insight") appears used in a very broad manner in the Pali suttas. Therefore "vipassana" appears to not refer to any specific or exact practice or experience; apart from being wisdom development in general. It appears the term "vipassana" can be used:

1. In very lofty ways, such as in MN 149 or synonymously in AN 11.2, to refer to direct non-thinking insight that occurs naturally & automatically (without an act of will) from concentration. Contemporary teachers, such as Bhikkhu Buddhadasa, have emphasized this lofty meaning of "vipassana" when they said: "vipassana cannot be taught".

2. In more shallow ways, such as in AN 10.60, where thinking or reflecting (paṭisañcikkhati) about impermanence (aniccasaññā), not-self (anattasaññā), etc, is used prior to direct seeing (ānupassī) of impermanence, not-self, etc. This type of vipassana (that Bhikkhu Buddhadasa called "suitable for people at a fairly undeveloped stage") is taught by contemporary teachers such as Mahasi Sayadaw and Western monk Yuttadhammo, where practitioners recite mantras such as "rising, falling, rising, falling..." etc.

Because the 2nd type of "vipassana" above continues to use thinking (paṭisañcikkhati), it may not or cannot reach serenity/samatha, such as literally described in AN 4.94, which says there are practitioners developed in vipassana but not serenity (samatha). The strong impression is AN 4.94 is not referring to a high level of vipassana because a high level of vipassana would end the asava (outflows) and fetters (as described in SN 22.59).

MN 19 clearly says even when paṭisañcikkhati is wholesome, the mind is far from concentration and, to reach concentration & serenity, the mind must be made quiet & still.

Also, this 2nd type of "vipassana" (such as "aniccasaññā") appears clearly included in many suttas, such as MN 62, MN 118 & AN 10.60, as a preliminary practise to Anapanasati. In other words, Anapanasati, incuding its 13th stage called "aniccānupassī", appears to be a superior or more lofty development than aniccasaññā (because, as said, aniccasaññā uses paṭisañcikkhati).

In summary, Anapanasati is the orthodox fruition of the Noble Eightfold Path, where mindfulness of right view maturing in letting go (vossagga) automatically results in knowing of breathing and the concurrent development of insight (vipassana) & tranquility (samatha).

Steps 3, 5, 6, 7, 9, 12, 13, 14, 15 and 16 of Anapanasati are vipassana.

Steps 4, 6, 8, 10, 11, 12 and possibly also 15 of Anapanasati are samatha.

Anapanasati is a method of meditation that uses the focus on breathing as a tool to connect and reconcile different layers of psyche: mental, emotional, and somatic.

Vipassana usually refers to a style of meditation that puts particular emphasis on registering subjective phenomena as they arise, morph, and eventually pass away - cultivating and refining one's ability to notice arising and passing away of even the faintest and/or shortest subjective experiences and states, without getting carried away by them.

Anapanasati includes an element of vipassana, discovering things that go on in one's mental continuum, but it also assigns equal importance to cultivation of calm, non-scattered, and emotionally positive state of it mind.

Vipassana, on the other hand, insists that all attempts at manipulating and conditioning one's state of mind are counterproductive and instead claims that the very act of watching one's phenomenological continuum provides all the necessary material one may need to attain The Goal.

In practice, the two meditation styles start from two different points and get progressively closer as one's practice matures, becoming essentially the same practice at the advanced stages.

I don't think either one can lead to Nirvana by itself, in fact you have to absorb a lot of other teachings by Buddha and Buddha's students to know what it is that you're doing.