= é o mesmo que == quando dentro de [[...]] . De acordo com a mais recente página man , em SHELL GRAMMAR > Compound Commands > [[ expression ]] :
The = operator is equivalent to ==
e mais abaixo, em 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: