In what way are race and species different from each other?

You said it there. Species is a scietific term 'race' is not.

The classification is: Kids Preffer Cheese Over Fried Green Spinach

Kingdom, Phylum, Class, Order, Family, Genus, Species.

There are also sub categories in there and yes subspecies or variations are sometimes given a seperate latin name. Humans however are not classified that way.

Cuz all modern day humans are literally the same species we're all homo sapiens . With animals there are actual biological differences between species some of which would outright make breeding impossible or non viable for example polar bears n grizzlies can mate but the resulting offspring would be infertile and possibly have some issues while no matter where we take the two humans from they can breed together and the resulting offspring would be normal barring possible genetic diseases passed down from either parent, also when it comes to a species for animals we can usually still divide them into subspecies with their own intricate differences while humans can't be further divided since we're the last subspecies of human alive

Race you can successfully fuck. Species your probably going to get some weird flu and mutant baby.

Yes and no.

There are many different definition of "species" which have different levels of utility depending on the use-case.

For example, Mahr's defintion, which I usually favour is based solely to the degree two which two entities can interbred. As such, dogs, coyotes, dingoes, and grey wolves are straight-up the same species; and golden jackals are only partially speciated from them. There are a few advantages to this model - first, it's completely objective and not affected by time, space, or whim (Linneaus classified wolves and dogs separately because "dog tails go up"). It's also one of the few that doesn't get ugly when applied to humans - e.g. Neanderthals were human, full stop, to say nothing of any current population.

However, it also means that polar bears and grizzly bears are the same species too - not great from a conservation perspective. Likewise the dog/wolf/coyote/dingo bit.

"Race", I will defend, when it is understood to be a rough descriptor of one's lineage, at any scope - and this is what Darwin meant by "races of cabbage". So, forgive the fictitious example. Aragorn from Lord of the Rings is of the race of Men, the race of Numenoreans, the race of Isuldur, and the race of Elendil.

As such, there will be some population-level correlations - this is how forensic anthropology works, with various population markers giving you a series of "therefore probably" answers that are very helpful, but never absolute.

So, getting back, bears don't travel the world like we do, and human history is really quite short, and there have been very non-trivial migrations throughout, so we don't have the same isolated breeding populations, and not for the same time scale as, say, bears.

Partly because the rarity of interbreeding bears makes them a little difficult to study. 

 To qualify as the same species, two organisms need to be capable of producing fertile offspring. There are some animals that can hybridize just fine, but those hybrids are partly or completely sterile; for example, lions and tigers can produce ligers, of which the females are fertile but the males are sterile. 

 Race, on the other hand, describes genetic groupings within the same species, and in pure scientific terms is essentially synonymous with "subspecies". To give a non-human example, dogs display a very wide degree of physical variety that are all still mostly capable of viable reproduction, and were relatively recently discovered to still have that kind of compatibility with some wolves (and had their scientific name changed from canis familiaris to canis lupus familiaris in recognition of the common species). 

 Thanks to convergent evolution, we can't simply assume that animals that look or behave similarly are, in fact, the same species or even related. There are at least eight different families of tick in North America, for instance, all of which evolved separately and are very likely genetically incompatible with each other, despite sharing the same basic arachnoid traits and obligate hematophagy; the strategy of latching onto a bigger organism and draining its blood for sustenance is just that good, apparently. (See also the meme of carcinization, or as it's known to the layman, "Nature's irresistible urge to make more crabs".) 

 Given that, until we actually see various kinds of bears interbreed, we haven't really got any way of knowing if they're the same species of different subspecies, or different species altogether. And without forcing the issue, bears are naturally competitive with one another and don't generally lend themselves well to interbreeding, regardless of whether they have genetic compatibility or not. 

That said, new evidence is rolling in all the time, and there have been both sightings in the wild of grizzly-polar bear hybrids and a few in captivity, which may or may not be fertile. The classification might change if we start seeing clear family lines.

Back in the day, Species was taught (with onsie-twosie notable exceptions) as (paraphrased) " The ability to reproduce viable offspring. "

Asian man impregnates Black woman. Produces viable offspring that can grow up, reproduce, and pass on the genes? Same species.

Chimp mating with Gorilla? No viable offspring can ever be produced. Different species.

Race ... if it defineably exists ... would be thought of more like breed. Two breeds, say a Beagle and a Bulldog are different breeds, but being same species and therefore can still produce viable offspring.

This is how we were taught waaaaasy back in the dark ages of the 1970s.

Because scientists sold out to political correctness. As a biologist, I collected old textbooks once upon a time. What was done to Watson was an abject lesson and a warning.