Into is a single preposition showing movement or transformation — walked into the room, turned into a frog. In to is two separate words that happen to sit together, usually where "in" belongs to a verb — she gave in to the pressure, log in to the site.
The core difference
A preposition, and a coincidence of two words meeting.
- into — movement inward or transformation: drove into town, translated into French.
- in to — "in" belongs to the preceding verb: gave in to, turned it in to the office, log in to.
The test
Ask whether in belongs to the verb. "Give in", "turn in", "log in", "check in" are phrasal verbs — the in is part of them, so to stands separately. If the verb works without in, you want into.
The one that changes meaning
"She turned herself into the police" and "she turned herself in to the police" mean startlingly different things. The first is a transformation; the second is a surrender. That is the clearest illustration of why the space matters.