I have seen long sonatinas though I don't remember one.
I have seen short sonatas. Mozart's first piano sonata is extremely short, much shorter than his more famous Sonata Semplice AKA Piano Sonata K 545.
In fact, I am not so sure it should be called a sonata. It is definitely not in sonata form(no recapitulation as far as I can tell).
Here is what I am talking about:
I think a more appropriate name would be Suite no. 1. But no, it is Piano Sonata no. 1.
So why is this considered a sonata? It is super short and it is not in sonata form.
I am not even sure that Sonatina no. 1 is appropriate because again, it is not in sonata form.
I can understand why Violin Sonata no. 1(Mozart's very first sonata) is a sonata. It is in sonata form and there is a definite recapitulation in the first movement.
And how could you tell if a piece in sonata form that is like Piano Sonata no. 1 in terms of length is a long sonatina or a short sonata? Those 2 overlap so some sonatinas are more like sonatas and some sonatas are more like sonatinas.