Did people realize the similarities between our beloved housecats and their wild cousins before the advent of the theory of evolution?
The ancient Greeks and Romans had the opportunity to observe both wildcats (including great cats) and domestic cats, most of which originated in Asia and North Africa. However, they did not separate animals into neat and precise categories resembling modern classifications. They also were not as concerned with the origins of animal life and the natural world as they were with the origins of mankind, gods and culture. That's not to say that there weren't mythological origins for specific animals, just that there doesn't seem to have been much interest in the general origins of life itself besides the generally accepted hypothesis of spontaneous generation. As a result, early taxonomic thought focused on observed similarities between animals rather than biological relationships or shared origins. Aristotle divided animals into taxonomic categories based on physical traits, and most naming conventions also focus on the features and behaviors of the animals they describe.
For example, many names of animals derived from some physical trait (body shape, colour, skin, teeth, etc) or behaviour (calls, habitats, hunting or reproductive strategy, etc). Many words were used to describe animals which overlapped in general appearance and observed behaviour. Because of this, the Greeks and Romans did not make as sharp of a distinction between various species of large feline and feline-like animals, including some species of what are now classified as felids and mustelids.
Greco-Roman artists and authors frequently confused and mixed up traits associated with various animals, such as portraying "tigers" with spots, or mixing up the patterns of cheetahs and leopards. Many relied on sketchbooks or second and third-hand descriptions of animals which they had never seen themselves. When they did have access to these animals, it was often as part of a spectacle like an arena-game which was not very conducive to scientific observation. Given the extent to which Greek and Roman authors relied on hearsay and limited opportunities to observe these animals, it's unsurprising that many inaccurate beliefs proliferated.
The words leopardos, panthera, pardis and varia should be understood as umbrella terms for large cats, although in modern taxonomy they can refer to specific species (and in the case of Panthera a genius). Leopard and panther were especially common catch-all terms for big cats (lions, leopards, cheetahs, etc) and possibly similar spotted animals. The term panther may even have been used for genets which had similar enough silhouettes and spotted coats. This all makes it difficult to positively identify references to these animals in art and literature.
Lions were one of the best known species of cat to the Greeks and Romans, but they too were occasionally depicted with inaccurate traits. For example, the "Tomb of the Lionesses" depicts a large cat with a spotted body and striped legs. The differentiation between maned and unmaned lions in Roman literature implies that some "unmaned lions" may have been leopards rather than just female lions. Pliny's "Syrian lion" is described as having a black coat, making it very probably a melanistic leopard (commonly referred to as a black panther). Strabo and Agatharchides describe an Aethiopian "ant-lion" (not to be confused with the insect) with backward facing genitalia, but otherwise resembling lions.
Strange hybrids and mythological creatures are also described in the art and literature of the ancient world, including scholarly works. Ancient authors placed these right alongside real animals, and made connections between them. Hence, Herodotus reports on the existence of giant gold-mining ants from India (clearly mythical). Other creatures were likely misunderstood and garbled accounts of real animals. The manticore may have been a heavily corrupted account of tigers, as Pausanias surmised. Ambiguous animals, not easily identified by modern scholars, are also described in ancient literature. The thōs was often compared to a jackal, but sometimes a tiger. It's been tentatively identified as either a civet, ermine or hyena by modern scholars, but ancient accounts relate a wide variety of descriptions and identifications for it. The corocotta was described as some type of dog-wolf or lion-hyena hybrid, but was almost certainly actually a striped or spotted hyena.
A number of authors have tried to unravel a few strange descriptions of lynxes in ancient literature. The physician Galen wrote about the anatomy of primates, including their similarities to humans. He listed a number of species most similar to humans, referring to one by the term lynx. He wasn't the only ancient author to describe "lynxes" that are clearly apes or monkeys, although it's unclear why. Caracals, and possibly servals, were also confused with lynxes which makes much more sense given the physical similarities.
Despite all these comparisons between large cats and uh, non-cats, they didn't strongly associate domesticated cats with their larger cousins. This is probably because domesticated cats were not well known in Europe until the Hellenistic / Imperial Roman period, when they were introduced from Egypt. They were also much less popular than dogs and weasels (another domesticated rodent killer). Because of this, the domestic cat is simply not extremely common in art or literature. The Greek word ailuros is usually translated as a domestic cat, but also referred to the weasel and similar pets. The same is true of the Latin felis, from which feline is derived. It's easy to see why this comparison would be made, considering the similarities in size, appearance, and relationship to humans.
There's better evidence for the ancient Egyptians associating domestic cats with great cats. Various cults associated with feline deities included domestic cats, lions and cheetahs into their iconography. The goddess Basket was originally depicted as a lioness, before gradually becoming associated with the domestic cat. This is hardly surprising given how much more important both domesticated and wild cats were in ancient Egypt, their greater level of familiarity with them.
#Sources
ANIMALS IN THE ANCIENT WORLD FROM A TO Z by Kenneth F. Kitchell
ANIMALS IN CLASSICAL THOUGHT AND LIFE Ed. by Gordon Lindsay Campbell