There are no similarities in meaning. 'To be subject to' means to be under the rule of and is normally followed by a noun. To be likely to means to have a high probability of doing and is normally followed by a verb

To... "change"? Bramwell's answer is good, but I could see having some confusion if you read something like "conditions are subject to change". It just means they're allowed to change them, but they don't have to with any high probability.

You could say "I'm subject to hay fever in the Spring" or "I'm likely to have hay fever in the Spring" and there wouldn't be much difference in the meaning. Perhaps "being subject to" suggests more certainty: "I'm subject to his commands" versus "I'm likely to follow his commands". Also the sentence construction is different, so you can't just substitute one for the other.