An axiom is known to be a statement that is considered to be one of the things that are said to be true. This is something that is based on logic. The thing that makes this different from the usual fact is that this can be very self-evident. This means that the person knows that this is true based exactly on facts.
This means that this is considered to be accepted but there is no practical way to actually prove it. A theorem is known to be the statement that is based on axioms and other logical connectives. Take note that the theorem should be based on some logical connectives.