why sometimes I feel they are similiar?why sometimes I feel there is an obvious difference between them?why I can say我不是学生？why I can`t say 我没是学生。
Obviously, this is a common mistake made by my students too. This is a very useful website which explains the Chinese grammar points in English. I got many of my teaching ideas there. https://resources.allsetlearning.com/chinese/grammar/
This is the summary of the differences between ‘不’ and '没'.
* is used for negating in the present and future.
* is used to negate habitual actions
* is normally used with adjectives
* is used to ask questions
* is used almost exclusively with some verbs ( Correct: 不是、不在、不知道、不认识 ; Wrong: 没是、没在、没知道、没认识)
* is used to negate past questions
* only 没 is used to negate 有 ( Correct: 我没有（没）钱、他没（没有）车 ; Wrong: 我不有钱、他不有车）
* is used to make comparisons
You may refer to the website for detail description.
All the best, Gengruiliang.
@CK Leow: “没在” and "没认识“ are wrong? This is quite surprising to see, because I've definitely heard them used before! Here are just a few examples from jukuu.com
Is this a kind of non-standard useage similar to "ain't" in English?
Of course, 没在 is seen all the time when 没 and 在 are part of different phrases (ie. the 没 negates a verb after the adverbial phrase). But that's not really the same thing.
不 is adv, 没is both adv and verb,
so you don`t add a noun behind 不 directly, but you can add a verb behind 不 directly，
you can add a noun behind 没 directly，you can add a verb behind 没 directly too。
however，there is a special case, 没有 is a fixed set, 没and 没有 have the same meaning, 没有 is also a verb;
不是 is a fixed set too,
you can`t speak 不有、没是，
不有、没是 is never correct
when we read 没 mo4, 没 means "to sink", or "to submerge"