Starting pitchers have Games Started ("GS").
In the modern era (roughly 1985-present), closers have Saves ("SV") and Games Finished ("GF"). They do not have GS. Middle relievers have few or no GS, and few or no SV.
The rare "openers" will have GS but relatively few innings pitched ("IP"; usually around 1-2 IP per game). They are basically relievers except they start the game.
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Take
Rick Honeycutt as an example. Honeycutt was a starting pitcher early in his career - from 1978 to 1987, you see that he started 265 games out of the 299 he pitched in. From 1988 until retirement, though, he was exclusively a relief pitcher, never starting a single game. He did end some games and earn a few saves - he was never a closer, though, because of his teammate Dennis Eckersley (who earned lots of saves for the A's).
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Closers did not exist before about 1985. Relief aces, or firemen, often ended games and earned saves, but they also sometimes pitched in middle innings in critical situations, and sometimes started games as well (this was more common before the late 70's and 80's, and usually they were converted into starters full time, like Goose Gossage and Hoyt Wilhelm - experiments that did not last - or Wilbur Wood).
Before the 1960's, relief pitchers were usually younger and unproven pitchers, older has-beens, or depth guys. The save had not been invented as a statistic (though saves have been retroactively applied to pitchers).
The earlier you go, the fewer relief pitchers existed, and they basically did not exist at all until about 1910 (Doc Crandall is sometimes considered the first relief pitcher). Relievers were starting pitchers pitching on their off days, or one of your stable of pitchers who were not proven (whether younger or older) and sometimes got starts anyway (Crandall pitched 185 games from 1909 to 1913 - he started 53, came in as a reliever in 132, and finished 120).