Politician, statesman, politico are comparable when they denote a person who is versed in or engaged in politics or in the science or art of government, though they are often regarded as contrasting rather than as interchangeable terms.
Politician regularly implies a personal and professional interest and a party affiliation and stresses to varying degrees the resulting bias; it is likely to suggest ability to deal with masses of people so as to accomplish such desired ends as election to a political office whether of oneself, or of one’s chosen candidate, or the passage of bills or the acceptance of measures one upholds, or the settlement of especially difficult problems to the satisfaction of one’s constituency or of the country as a whole.
Sometimes politician is used with a strong suggestion of derogation or contempt to imply scheming, self-interest, artifice, or intrigue in accomplishing one’s ends.
Statesman implies elevation above party conflict and a mind able to view objectively the needs and problems of the state and its citizens and to concern itself with the long-term greatest good of the greatest number. The term, often in contrast to politician, is likely to stress both eminence and ableness.
Politico is virtually interchangeable with politician but perhaps more likely to stress concern with partisan political activity than with the actual business of government. Like politician , it can be highly derogatory.