Evolution claims common descent, that is all life forms are related to each other via a common ancestor. Every living thing shares a granddad—if we go back far enough, or put more scientifically, universal common ancestry.
The alternative is known as fixity of the species, species don't change. Of course species do change, every offspring is different to its parents. On a population level gene frequencies change and mutations arise. So fixity of the species cannot mean change does not occur, rather that it is limited. So how does one define species?
Unfortunately the number of definitions is somewhat large, and much depends on what you want your definition to do. If you favour evolution, then definitions more in line with the theory may be favoured. A creationist could do the same.
From a creationist perspective I would favour the definition of species to be that of the fundamental types of plants and animals God created to breed with each other. A tree with fruit producing seed after its kind (Genesis 1:12). Beasts after their kind (Genesis 1:25). This is the basis of baraminology.
How do we work this out in practice? Some of the animals extant are different in some ways from their likely forebears, though many bear striking resemblance!
Linnaeus was onto something. Unfortunately it seems his species and even genus categories were not broad enough. We do not have fixity of the species if we use the Linnaean taxonomy.
If we start with created kinds that can breed, changes over time may limit reproduction. For example changes in body size, or timing of fertility, or cellular incompatibility may preclude breeding. These changes may come about by genetic changes such as allelic loss, mutation, targeted adaptability, chromosomal rearrangement. So while I dispute a species definition based on isolated reproductive populations, such populations may in fact be unable to breed when reintroduced to each other.
It seems likely that the various feline species descended from a pair (or group) of cats with great capacity for variation. The same with cattle, dogs, bears, and so on. Such variation can be seen in the size difference between a lion and a domestic cat, and the coat differences between tigers and leopards.
The best working definition for "species" (or type, or kind, or baramin) would consider hybridisation. Organisms that can produce offspring whether sterile, fertile (partially or fully) would be included within the same species group. A corollary of this is organisms that share hybridisation partners (however distant) would be grouped together.
This would greatly reduce the number of species, and each species would show significant variation, but the species would be isolated from each other. Tigers, leopards, lions, jaguars, lynxes will all be grouped together, but they would remain completely distinct from bears or parrots.
This is similar to fixity of the species. It allows for greater variety than is usually envisioned, though not an alien idea if we ponder domestic dog varieties. It allows for speciation in that subsequent populations may lose breeding capacity with each other, though at the cost of decreased genetic diversity, and no capacity to generate fundamentally new organisms. Some may dispute this definition of fixity of the species by reason that such groupings are frequently at the level of family or even order, or that non-interbreeding populations may arise. Fine, I am committed to the concept, not the name. "Inviolable organism boundaries with capacity for significant adaptation" is adequately descriptive though not so eloquent.