They're different, believe it or not.
We often hear cooking-show hosts talking about popping something "in" the oven. Well, probably the only thing we can pop IN the oven is popcorn. What they should say is, "pop the dish INTO the oven."
"Into" describes an action, a direction toward the inside of a place, like jumping into a swimming pool; whereas "in" describes a location…in rather than out of a place or outside, like in the water of the swimming pool.
So…what about "in to" — not "into"?
"In to" might also involve an action, such as "I turned my test paper IN TO the professor."
Or "He refused to give IN TO the kidnapper's demands."