Are double and single quotes equals? Can they be used interchangably?
Which are used most often?

If you are asking about assembly source code for fasm then for the most part, yes. Don't know. Popularity doesn't matter.

You can use double quotes if text contains single quotes and vice versa for convenience not to bother with escape sequences

>If you are asking about assembly source code for fasm then for the most part, yes.
Yes. Why for the most part, are there exceptions?

If you change the quote character then ...

• They look different in an editor.
• The files will hash to different values possibly affecting your SCM.
• Concatenating things with macros may change the results.
• Probably more things I can't think of right now.

Changing between single and double quotes has no effect on macros, because both methods lead to the creation of identical "quoted string" token and macros operate on tokens, not original text. The only real difference is the one mentioned by zhak, that you use can freely use a single quote inside a string enclosed with double ones, or vice versa.

Well, another difference is that the single quote is allowed in numeric symbols, while the double quote is not, although none of these forcefully starts a new symbol and both can therefore be freely used in non-leading positions of other symbols such as constant names. They are treated then as different characters, of course (a"b = 1 defines a constant other than a'b = 1).

P.S. And the string-enclosing quote can also be used inside the string if put twice in succession.