~$ cat test
(( $1='this' || $2='that' )) && echo test1 says ok
(( $1=='this' || $2=='that' )) && echo test2 says ok
[[ $1='this' || $2='that' ]] && echo test3 says ok
[[ $1=='this' || $2=='that' ]] && echo test4 says ok
~$ test wrong wrong
test: line 1: ((: wrong=this || wrong=that : attempted assignment to non-variable (error token is "=that ")
test2 says ok
test3 says ok
test4 says ok
~$ test this wrong
test: line 1: ((: this=this || wrong=that : attempted assignment to non-variable (error token is "=that ")
test2 says ok
test3 says ok
test4 says ok
~$ test wrong that
test: line 1: ((: wrong=this || that=that : attempted assignment to non-variable (error token is "=that ")
test2 says ok
test3 says ok
test4 says ok
~$ test this that
test: line 1: ((: this=this || that=that : attempted assignment to non-variable (error token is "=that ")
test2 says ok
test3 says ok
test4 says ok