We are aware of 16 known breeds of Khajiit plus the unique breed that is the Manes, but there's been a lot of confusion in the fandom about how senche-cats, senche-tigers, the supposedly more than 20 breeds of Khajiit fit into this. What is the full count of Khajiit breeds, and what are the gradations between Khajiit and ordinary cat? Allow me to offer my own thoughts on this complex matter.
There appear to be three main gradations of cat: Khajiit, semi-Khajiit cats that are related to the Khajiit, and non-Khajiit cats that are either not related to the Khajiit or very distant relatives of them. An example of this are the various gradations of "senche", the Khajiit term for large quadrupedic cats that are not pahmar. There are true Senche (and Senche-raht), which are members of the Khajiit species. Then there are Senche-Cats, which I take to be one species divided into a number of subspecies including senche-panthers, senche-lions, senche-tigers, senche-leopards, etc., being further divided into different breeds such as Black Senche-Panthers and Striped Senche-Panthers; Senche-Cats can have fertile offspring with members of other subspecies, and they are related to both Khajiit and non-Khajiit cats (including Sabre Cats), sharing Khajiit's taste for moonsugar and strong connection to the moons. It may even be possible that Senche-Cats can successfully breed with both Khajiit and related non-Khajiit species of cat (for example, senche-lions and normal lions may be able to procreate). Finally, there are what I call "raht-cats", which may or may not be able to breed fertilely with Senche-Cats but who would struggle do such even more with Khajiit. Raht-cats are my collective term for species of the subfamily Pantherinae which exist in our world as well as in The Elder Scrolls universe. These include leopards, tigers, lions, etc., of the ordinary variety. They are all big cats and related to Senche-Cats, but unlike Senche-Cats cannot create fertile offspring with each other (for example, lions and tigers can't create fertile offspring), and raht-cats lack a connection to the moons or a taste for moonsugar. And finally finally, you also have ordinary house-cats and similar small cats, but you may be able to lump them together with raht-cats in the category of totally non-Khajiit cats, and yet alternatively, since house-cats do not exist in the wild, all house-cats on Tamriel may in essence be semi-Khajiit "Alfiq-Cats", similar to how "Senche-Cats" relate to Senche Khajiit; after all, The E.S.O. goes as far as to call the housecat 'a distant relative of the Alfiq Khajiit.'
Next on the agenda is the confusion surrounding the term "senche-tiger". As previously explained, terms such as "senche" and "tiger" can both be extremely flexible. A Senche-tiger may merely be a Khajiit Senche with a tiger-shaped pattern, whereas a senche-tiger is a subspecies of Senche-Cat which may also be classed as a tiger; even Pahmars, which while mostly quadrupedic are explicitly not senche of any kind, are sometimes described as "tigers" or "tiger-like" (not to mention the "tiger" species of Po' Tun native to Akavir). Tiber Septim even called striped guar "tigers" (no joke :p )!
To keep things simple, I'm going to suggest that there are three basic kinds of Senche-Tiger. The first, Senche-tigers, are as previously explained Khajiiti Senche which have tiger-like patterns. The next are senche-tigers, which are a subspecies of Senche-Cat and can come in a number of breeds. Finally there is one more type which I call "senche-tiger-raht" and whose origin is more speculative. This is an unproven hypothesis on my part, but my guess is that just like Khajiit come in both "normal" and "raht" varieties, so too do Senche-Cats. Senche-Cat-raht are much more monstrous than their more easily domesticated normal senche-cat cousins, and somewhat resemble Khajiit Senche-raht but are distinct from them; therefore if you were to compare a Senche-raht-tiger (a Senche-raht with a tiger-like pattern) and a senche-tiger-raht side-by-side, the differences would be obvious. Despite being more "savage" and "wild" than their civilized Khajiit cousins, they are probably as intelligent as any Khajiit, blurring the line between Khajiit and non-Khajiit more than any other being, such that the Khajiit may consider them to be "feral" varieties of themselves. Maybe there are Alfiq-Cat-rahts too: Who knows? ¯\_(ツ)_/¯
Assuming though that the count of "over 20" breeds of Khajiit do not include these hypothetical, Senche-Cat-raht, borderline Khajiit, then what are the remaining breeds of Khajiit? Depending upon whether the moons are full, waxing, new, or waning, a different breed of Khajiit is born (Manes are born on special occasions of lunar alignment). But what if the moons are between these states, which is to say when the moons are crescent or gibbous? This may be when very rare breeds of Khajiit are born, specifically four breeds of Khajiit corresponding to two different moon-states (gibbous and crescent) and the pairs of a gibbous Masser and a crescent Secunda and of a crescent Masser and a gibbous Secunda. The interval of time during which a Khajiit baby must be born to be one of these rare breeds must be finicky, though, since being born too close to the stages of new moon or full moon leads to the birth of one of the more common varieties of Khajiit. Therefore, the states of waning gibbous and waxing crescent may be the only ones that correspond to rare breeds, as the states of waxing gibbous and waning crescent are very close to becoming a full moon or new moon respectively. The following are my best guesses as to what these four breeds are:
Dagi-raht-Senche: born when Masser is a waning gibbous moon and Secunda is a waning gibbous. They are medium-sized quadrupeds.
Alfiq-raht-Pahmar: born when Masser is a waning gibbous and Secunda is a waxing crescent. They are also medium-sized quadrupeds.
Cathay-raht-Suthay: born when Masser is a waxing crescent and Secunda is a waxing crescent. They are medium-sized bipeds.
Tojay-raht-Ohmes: born when Masser is a waxing crescent and Secunda is a waning gibbous. They are also medium-sized bipeds.
Conveniently, this gets us to 20 breeds of Khajiit, 21 breeds if we include the Manes, and even more if we include hypothetical senche-cat-rahts (or alfiq-cat-rahts) such as senche-tiger-rahts.
What do you all think of my theories? Definitely looking forward to feedback! :D