In fact this is a very good question.

不 = do NOT.

没（有） + verb = negative of past tense / negative of present perfect

我不戴手表 = I don't wear ANY watch (because of some reason). (Sorry but I have to say Nieves was wrong. "I don't wear my watch" is different from "I don't wear any watch".)

"I don't wear any watch" is a kind of state. For example, I hate all of watches so I never wear any watch. In this case, we say: I don't wear watch or I don't wear any watch.

"I don't wear my watch" is talking about a specific thing: I don't wear my watch because I like to wear other people's watch so I'm a thief :D

我没（有）戴手表 = I didn't wear my watch. / I haven't worn my watch.

e.g.

你去过美国吗？ ------- have you been in US?

我没（有）去过。----- No, I haven't.

不和没区别

什么是不和没区被

例如


我不戴耳环 （可以理解为我不喜欢戴耳环，我没有戴耳环的习惯）
我没戴耳环（可以理解为我现在没有戴耳环，可能是我不想戴耳环，也可能是我忘了戴耳环）

第一种表示不的感觉更强烈些。

我不戴手表。有两种可能，一种是我不喜欢戴；一般只是现在不戴。比如丈夫要出差，妻子把丈夫要用东西准备好，丈夫把手表拿出来，说“我不戴手表，有手机就够了。”

如果说成”我今天不戴手表。“也没有”我不喜欢戴手表“的意思。