The word "strangeness" was invented before the quark model have been developed. People started finding strange particles in particle physics experiments that they had never seen before. These particles seemed to hang around much longer than expected based on their other properties, before decaying into "normal" particles. Since these new particles were always created in pairs, people came up with the idea of a conserved quantity called "strangeness": the strange particles would always be created in pairs of +1 and -1 strangeness (since you would have started with zero strangeness) and then they would live for a long time because they can't decay into non-strange particles due to the conservation of strangeness. Of course, they eventually do decay, which suggests that the types of interactions that create them are different from the types of interactions that cause them to decay, and only the former obeys the conservation of strangeness law.

Nowadays, we know that particles with strangness all have a particular type of quark in them, which we call "strange" to match. Particles with -1 strangeness have a strange quark while particles with +1 strangness have its antiparticle. Furthermore, we know that the interaction that produces the strange particles is the strong interaction, which does not change the type of quarks, although it can create new ones in particle-antiparticle pairs. The interaction that causes them to decay is the weak interaction, which is the only interaction in the Standard Model that can change quark types. Since the weak interaction is a lot weaker than the strong interaction, the strange particles are able to live for a long time before decaying.

We could define a special quantum number for all of the quark types, and we would find that strong interactions always preserve that quantum number while weak interactions do not. However, now that we understand the mechanism underlying the pattern, it's never seemed particularly useful to do so.