When using == or != in bash you can write:
if [[ $t1 == *"$t2"* ]]; then
echo "$t1 and $t2 are equal"
fi
Note that the asterisks go on the outside of the quotes and that the wildcard pattern must be on the right.
For /bin/sh, the = operator is for equality only, not pattern matching. You can use case for pattern matching though:
case "$t1" in
*"$t2"*) echo t1 contains t2 ;;
*) echo t1 does not contain t2 ;;
esac
If you’re specifically targeting Linux, I would assume the presence of /bin/bash.