Answer by don_crissti for bash [[ = ]] behaviour

= is the same as == when inside [[...]]. As per the more recent man page, under SHELL GRAMMAR > Compound Commands > [[ expression ]]:

The = operator is equivalent to ==

and further down, under CONDITIONAL EXPRESSIONS:

string1 == string2
string1 = string2
        True  if  the  strings  are equal.  = should be used with the test command
        for POSIX conformance. When used with the [[ command, this performs pattern
        matching as described above (Compound Commands).

bash info page: