I would say they could be used interchangeably - or at least they all could mean the same thing. If you describe someone as reserved or introverted they are probably quiet and don't talk much. If you describe yourself as a person who keeps to myself, that may mean you are reserved or introverted but I would think it could also mean that you mind your own business. Perhaps it is slightly more situational - you might actually be somewhat extroverted but perhaps at work or engaging in some activity you 'keep to yourself' and don't pay attention to what others around you are doing.

I would say "introverted" is more of a personality trait, while "keeping to onself" refers to a behavior. In the right context, they could be interchangeable.

By implication they mean similar things, and can be used together. If someone ‘keeps to’ him or herself, then you might infer that he or she is reserved, or introverted. Is someone seems introverted, e.g. they don’t speak much in social situations, you might conclude that person is reserved and might tend to ‘keep to himself/herself.’ Here are some examples - ‘He’s quite introverted, he tends to keep to himself’. ‘He seems quite reserved’ ‘I think that’s just his manner - he’s quite introverted’ ‘Did you meet the new neighbour in flat 6?’ ‘No. She tends to keep to herself’ So they aren’t exactly interchangeable, for example in the last example the person might be avoiding others for reasons other than her being introverted so you couldn’t really say ‘she’s introverted’ or ‘reserved’ here, but they do all have similar meanings.

To add on to what Joe and Roxanne said, if you want to use the phrase "keep to myself" to describe someone, other than yourself, you would say: he keeps to himself, she keeps to herself, they keep to themselves.