is B sharp the same as C?
is E sharp the same as F?
is C flat the same as B?
is F flat the same as E?

If you are tuned to equal temperament, yes.

It also depends on context. Are you speaking about them as single entities, or are they part of a musical line within a polyphonic piece? It all depends on where you are coming from. You might be interested in reading about the history of the tempered scale in western music and about harmony. There are quite a few ways that musical analysis can be undertaken, so in some ways the notes you describe are the same in others they are totally different. Depending on how much you like to read, the journey can take you from European music history to world music , to physics and back. Definitely interesting stuff.

Technically, they are not the same. They just sound the same. When you`re playing something like the piano, that doesn`t matter...much. On a violin, for example, it tells you what finger to use. There are many reasons why composers use a certain note, and not another. It has to do with key signatures and stuff like that.