In baseball, pitchers are divided up into two different categories: starters and relievers.
Starters are pitchers who start the game and try to pitch as long as they can; if they pitch the entire game, it's called a "complete game". They pitch every 5 games and are generally better paid and known than the relievers. As baseball as evolved, starters have started pitching fewer innings, so complete games are less common and they usually pitch between 5-7 of 9 innings.
The remaining innings are pitched by relief pitchers; they're usually called the "bullpen". Modern relief pitchers will generally pitch 1 inning, and in uncommon situations, pitch 2 innings. There are specialist pitchers, usually left-handed pitchers who will come in for only 1 at-bat, if the manager wants to really try to matchup against a feared hitter.
Relief pitchers can pitch on consecutive days and aren't on a schedule like starters. Most teams will have 2-3 relievers that they really trust to do important innings and these are the ones who will be known to fans. If a pitcher pitches mainly the 8th inning, they'll be called the "setup man". If a pitcher regularly pitches the 9th and final inning, they'll be called the "closer"; if they pitch out the rest of a close game, they'll be credited with a "save". Closers will be the most famous and well-paid of the relievers.
During the time that Mayday Malone was playing, the "set-up" and "closer" roles were still being introduced, so it was more common for relievers to pitch 2-3 innings. This was also the time that the "Save" was introduced as a statistic and closing games would make stars out of the likes of Rollie Fingers and Goose Gossage. (also, it was a great time for nicknames it seems).
So, it is possible that even as a relief pitcher that Sam Malone would gain some renown if he pitched well for a few seasons.