They are essentially the same thing, though politician has a less positive connotation than statesman.

"Statesman" is complimentary. "Politician" is slightly derogatory. "Politician" and "politics" often suggest the processes of making deals, compromises, asking for campaign money, and perhaps a trace of corruption or at any rate special favors for cronies. You could NOT say "politician" here. "Ladies and gentlemen, it is my great pleasure to introduce to you a devoted public servant, a tireless fighter for the public interest, and the greatest statesman I have ever had the privilege to know: Senator Bumstead Boopfaddle!" You could NOT say "statesmen" here. "I see the politicians in Madison [state capital] voted themselves another pay raise yesterday."

In Taiwan, police officer is more like a security guard to protect statesman means politician or government.