They can mean the same thing in some contexts. But usually, "check in on" would be used like "check up" as if you are their doctor or carer; while "check in with" would be used on equal terms, like a balanced catch-up chat with a friend or colleague, or for checking in to a hotel together.

Yes, they are different. The first one can be used in a medical setting or a casual setting with a friend. For example, if a friend tells you they are sick, later during the week, you might message them, “hey, I just wanted to check in on you, how are you feeling?” Someone else who is friends with this person might say, “hey, I heard this person was sick, have you checked in on them? I might make them soup or something.” If you go to the hospital for an annual visit or a regular appointment, the doctor might say, “hey, I wanted to check in on you, how are things? How are you feeling?” The second one is more administrative, related to business. For example, if you had a question at work but no one had an answer, someone might say, “hey, did you check in with John yet? He might know.” You “check in with someone” when you speak to someone to confirm something or learn new information.

They are different, but neither has a precise meaning. Your meaning is more clear if you stick with just one preposition. It's better if you only use "check in" if you're really checking in. Otherwise, say "check on" instead of "check in on". "Check in on" is sloppier but conversational.

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