Maybe they used to be the same phrase but now they are used differently. “Into” is almost always used with entering “I stepped into the room” or “I delved into this topic of study” but there are other strange cases like the interest use “She is into him” (meaning: She is very interested in him romantically) or “I got really into the book.” I’m having a hard time remember how often I see “in to” used. Here are a couple examples “We stepped in to view the house” (meaning: We stepped inside in order to view the house). Here “in to” isn’t one phrase but its actually stepped in + to view.