Buddhism is practice differently in the west is because westerners usually have a skewed understanding of eastern religions, and vice versa.
Buddhism very simply put is the practice to achieve liberation, a state peace of mind, state of enlightenment, peace with the world, or Nirvana with absences of greed, hatred, and obsession.(IMO the devotion to study scripture, meditation, etc itself is obsession). You can simply say this is when someone has became a Buddha, achieved Buddhahood. Buddhists do not worship a supreme being, unlike Abrahamic monotheist religions, or multiple supreme beings, like in the case of Hinduism, or Taoism.(or Greek God & Goddess, nowaday labeled "mythology" by modern day religions). So Buddhism is an non-theistic(atheistic) religion, where there is lack of belief of deity.
Taoism is broad. What you commonly see in China and many parts of Asia is Chinese folk religions, including worshiping ancestors and many many deities. Under Communist rule, especially after the Cultural Revolution much of the practices have been abandoned and only in recent time China has seen a revival of building of temples. They are unique Chinese cultures. You will see much of this still in practice in much more depth in Hong Kong, Taiwan, or Malaysia where there's large Chinese population outside of the Cultural Revolution.
Confucianism is the teaching of Confucius philosophy. I'm not even sure that is a religion. But why do some countries have ceremony for this Confucianism? or even worship Confucius? IMO governments use Confucianism as a way to govern. Same as with many countries with state religions, using organized religion to rule their citizens.
I'm a secular humanist/atheist. I see religions as ways of life people choose(were forced, or scared into) to follow. But the more I learn about Buddhism the more it's making sense to me. We'll see.
I know I've only scratched the surfaces of these two religions. I hope to hear more people chime in on this topic too.