See, that's where it's fuzzy.

I've heard it used the same way as subspecies, but also as simply to refer to variants within a population, that haven't split off into their own populations, like, say, black wolves amongst grey/timber wolf populations, or redheads within northern teutonic/saxon/celtic populations.

Two races can hybridize into their own populations as well, such as Metis or Mexicans, amongst humans, or like I remember seeing Red Wolves might be (a self-sustaining group of coyoteXwolf descendants), or the European Wisent (genetically discovered to be a cross between an extinct relative of the North American bison and the Aurochs.)

Real speciation can only really happen if there's a long enough break in geneflow for genetic drift/adaptations to take enough effect to hinder the two populations from producing offspring that are both viable and fully fertile. (viable meaning they don't tend to die before being able to breed, fully fertile means they can breed with either parent species, or each other. Horses and donkeys are two different species because while mules and hinnies are viable, they're not fertile. There's a species of European crayfish that split off from another species about 25-30 years ago, but the new species is completely parthenogenic; they produce clones of themselves and do not/cannot mate with the males of the parent species.)

Strain or variety could also refer to what humans think of as bloodlines, or breeding lines.