The concept of "strangeness" came before the idea of the strange quark. In the early 1950s some newly-discovered particles had longer lifetimes than expected, so they were called "strange" and a new quantum number, "strangeness", was invented for them. The strong and electromagnetic interactions conserve strangeness, but the weak interaction doesn't.
In the 1960s the idea of quarks came along. Originally there were only three of them: up, down and strange. All the "strange" particles have a strange quark in them, and a strange quark can convert to a down quark only via the weak interaction, which explains the long lifetime of "strange" particles.
The charm and bottom (originally "beauty") quarks came along later, in the 1970s, to explain more newly-created particles that have properties that don't fit into the old up-down-strange scheme.
Finally, based on the pattern formed by the up, down, strange, charm and bottom quarks, it was widely assumed that a "top" quark also had to exist, but particles containing top quarks weren't actually observed until the 1990s.
In the meantime some physicists speculated that maybe top quarks weren't really necessary after all. I remember seeing in the early 1980s, towards the end of my graduate-school period, preprints about "topless bottom models" which sounded a bit, um, risqué.
