In English, "active" can mean both "not switched off" and (for example) "runs around a lot". Aktiv also has these meanings. Tätig is more specifically associated with doing stuff (i.e. not the first meaning).
So, if you are tätig then you are also aktiv. But it's possible to be aktiv without being tätig.
Yes, it would be ambiguous between the two meanings. It's common for "Sie" to have two possible meanings in a sentence, and context would dictate which one is meant.
(As another example, "Ich liebe sie" could mean "I love her" or "I love them." Again, context would have to determine which was intended.)