These words cause us problems. Let's see whether we can clear some of those up.
The words in and on suggest a location. We are "in" the room. It is "on" the table. When followed by the word to, the word to is part of a prepositional phrase or an infinitive.
...went in to cash my check...
...moved on to another town...
...went on to bigger and better things...
The one-word forms always imply movement. Something or someone was not there before and now is.
We were not in the room before; we walked "into" the room.
It was not there before; we put it "onto" the table.
...deposited it into the bank...
...turned onto the roadway...
...put the money into my purse...
...held onto the handle...
There is an idiom that we have to deal with -- turn into. With one word into, this expression means "to become." So when it does not have that meaning, it has to be two words.
...When he drinks, he turns into a monster.
...He turned in to the driveway.
...pulled into the driveway...
...moved into the driveway...
...turned in to the driveway...
One-word/two-words issues are discussed in Chapter 29 of my book.
Happy punctuating.
Margie