Certainly not all Chinese lathes – there are those you can park a car on and some you can park a bus on…
I suppose there are 'mini lathes' and 'Mini Lathes'.
A mini lathe is any very small lathe, probably less than 3 1/2" centre height, and would include Unimats, Taig/Peatol, C0/Baby, C1, Cowells 90 regardless of origin, but probably not including 'watchmaker's lathes'.
I wouldn't actually call any 3 1/2" lathe a 'mini lathe' as this is generally accepted the size that is needed for 'typical' model engineering tasks – few people would classify a 7-series lathe as a 'mini lathe' (although there are some people who use the expression as synonymous with 'hobby lathe' – but where does hobby machine end and professional machine start, clearly they overlap.)
BUT…
In the early 90s a small lathe design came out of Russia which was copied in China by various manufacturers as a standard design. By the end of the decade had become widely available in the UK.
It had a respectable 3 1/2" centre height, but originally only 10" between centres, though soon many 12" versions appeared.
These 3 1/2" x 10" (or 7×10 machines as they were known in the USA) were much more 'compact' than typical model engineer lathes (i.e. the 7-series) and the name 'Mini Lathe' was used and became the accepted name of these machines and their descendants, some, but not all, being sold under this name or at least with it on their labels.
There are now 3 1/2" x 16" versions which can do most things a 7-series can do (aside from not having a gap bed), I would argue 'compact lathe' would have been a better name for these as it reflects modest overall size rather than limited abilities. But the horse bolted twenty years or more ago!
Some people apply 'Mini Lathe' to larger machines like the SC4 and even larger machines. I think this is very misleading, as the SC4 is somewhat bigger than 7-series in centre height with about the same between-centres capacity.
My advice is to use 'Mini Lathe' (in capitals) to mean C2, C3, SC2 and SC3 lathes and those of similar design like the Chester Conquest and Clarke CL300. This will confuse the fewest people, as it's what MOST people mean by 'mini lathe', although a 1999 brushed motor 7×10 C2 lathe doesn't really compare to a 2019 7×16 SC3 with brushless motor in terms of quality, capacity and capability…
For the very small lathes – I'd use 'small lathe' rather than 'mini lathe'.
Neil