When does a race become its own species?

I was wondering about this recently as a total layman when it comes to biology: How exactly is this determined? For example, it seems to me that the external differences between say a tiger and lion are far smaller than those between a St Bernard and a Chihuaha, yet the last two both count as dogs.

I assume it is because they can theoretically breed, whereas a tiger and a lion tend to produce infertile mutants. But in that case: Is there something "special" about dogs? Or could we, if we set our mind to it, theoretically breed handbag sized tigers?

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