What is the difference between learning the Buddhist way and simply learning from life?

Buddha probably thought buddhism was the best approach, or else he would have spent his time promoting something else.

The idea of "learning from life" makes me think of learning based on the rules of the society a person is born into. Most societies are deluded. It is more unlikely to just have an epiphany one day and realize this than it is to follow a set of instructions that have helped people have this realization for thousands of years.

This way of approaching life and escaping delusion exists without "Buddhism"; someone can figure out to follow the same approach as a Buddhist without ever knowing that Buddhism existed. This is why individuals can escape samsara even when the teachings have been lost. In the same sense, a person could rediscover algebra... but think how much easier it would be to just go to school and be taught algebra.

It's a complex question, with a lot of components needed for a complete answer. I'll offer just one.

A fundamental difference between Buddhism and "western thought" (as you call it), is that word "thought". A key part of Buddhism is you have to do it; it's not just a set of ideas to believe or reject. If your knowledge of western philosophy extends to the phenomenology of Husserl and Heidegger, think of Buddhism as, in part, applied phenomenology.

Analogy time. You can read all you like about weight training, cardio, diet, stretching and so on, but merely reading about them won't build your muscle mass or your endurance. In that sense, the bias in western thought makes it like reading about those things; Buddhism is more about doing them.

Oh, and in that context, the Buddhism/atheism thing is probably a false dichotomy. I don't necessarily agree with him, but see Stephen Batchelor's "Confessions of a Buddhist Atheist" and "Buddhism Without Beliefs".

Buddhists believe in rebirth, gods, ghosts, hells, heavens, Karma. Atheists don't!

Paticca Samuppada, the Four Noble Truth and the Noble Eightfold Path are not taught in other religions.

Different religions have different concepts of enlightenment. What Buddhism teaches as 'Nibbana' can only be achieved by following the Noble Eightfold Path and realizing the 4 Noble Truths.

Nibbana is the deathless element. It is a permanent, peaceful state which is soulless. I don't think you get that definition in other religions.

The key difference is Detachment from the Event that you are learning from. Your life is a series of events, both good and bad. Through observing the "self" using Buddhist techniques such as Vipassana, you can witness your own emotional reactions to events almost as a third person. This helps create a balance in how you respond to events, promotes equanimity and empathy towards yourself. It takes the learning beyond what you would see through the lens of your emotions. For example, you will stop blaming yourself or someone else, and learn that an event was the natural transition from circumstances that were unavoidable. This philosophy of learning is also referred to as "Mindfulness".

Being an atheist you always deal with conceptual thinking even though you can be a very good person. But any happiness you get out of impermanent things is impermanent and thus is not absolute. It cannot be preserved when old age, sickness, death and loss come.

Being a buddhist you decide and work to reach a state of mind that is beyond any conceptions and that brings you to the state of absolute happiness. And out of that state you can also be best possible help for others. For that you take refuge (decide that it is most important for oneself) in the goal (Buddhahood), the way (Dharma, Buddha's teachings) and the friends on the way (Sangha). So it is about practicing Buddhas instructions to reach the state of a Buddha. Also being a buddist means you don't just believe in what Buddha said, but you try, practice and see if those instructions work in your case. It's about experience, not about belief.

You could say that Buddhism provides methods to use life as a lesson, every moment is a learning opportunity. That's why the texts and talks are called 'teachings' - by learning to change our perspective on life, we can deal with it more skilfully.

Does Buddhism recommend itself as the best approach to reach enlightenment, or can this fulfillment be achieved outside of Buddhist schooling?

Buddhism contains teachings that are singularly designed to help human beings get out of this endless wheel of suffering (in Buddhism called Samsara). By learning to see things from the perspective that There is suffering, Suffering is caused by craving/clinging, There's a way out of suffering and The path to end suffering is detailed [in eight 'components'] we can skilfully reduce our suffering/anxiety/dissatisfactoriness of our lives.

Most importantly, the Buddhist teachings were not designed to be believed in. The were designed to be used. So we can choose to learn the doctrine like any other religion, and believe it or not, or we can put the teachings to practice. Only then will they have an impact on your life.

Part of Buddhism ("being a Buddhist"), involves taking on five (or more) precepts, similar to other religions. These include refraining from killing, stealing, sexual misconduct, lying, and taking intoxicants. However, to practically train the mind, meditation is an essential component of the Buddhist training. There are thousands of techniques that can be put to use, most helpfully aided by an experienced teacher.

What is different about being a Buddhist than an atheist?

The question does not entirely apply, but suffice to say that atheists reject that there is any god that "rules the world" - Buddhist teachings include the existence of deities, heavens and hells (all plural), but that none of them "rule the world", that there is no one entity that decides over this existence. Important is to note that these deities are not worshipped as if they are above humans, and Buddhists have compassion for those in the hell realms.

NOTE: This is a very simplified answer in response to your questions. In summarizing this way, inaccuracies may have crept in, unintentionally. I encourage hearing more from a Buddhist, in person (ideally a monastic), to get a better understanding. (opposed to just reading about Buddhism)

It would probably take a book to adequately answer such a question.

Some of us would say there are different ways to the same understandings. And that understanding in such a context is not merely about philosophical insight, but involves the human condition in its totality.

But imagine a person trying to negotiate a maze. There are different ways of understanding the maze. The maze as it is experienced by someone trying to seek the exit and a transcendent perspective in which the maze is seen in its greater context. e.g. another person has a map.

These are different perspectives of the maze. However what should be understood? The maze, is only one aspect of this experience, another part is understanding the experience of being lost in the maze, of coping with such situations, and thus being able to empathise with others experiencing the maze.

Thus to really understand the maze different perspectives are helpful.

But note, the person who is lost in the maze may come to understand the maze eventually and create their own map, and thus come to understand the maze and find their way out.

Thus transcendence can inform immanence, but likewise immanence can inform transcendence.

Western understanding has tended to focus on the intellect and thinking, whereas in the East there has always been an understanding that thinking and intellect had to in some way be transcended in order to find a greater comprehension. But it is equally recognised that such an Eastern approach requires a fairly single-minded concentration on the search for "reality" or whatever, something which people with busy lives are unlikely to pursue.

Some would push one way at the expense of the other.I would say they are simply different approaches, and people gravitate to the approach that suits them in their life.