In this SO Question there is a comment by
A computer without loops is a calculator
Is this true?
Is that the only difference?
Is there a set of criteria to differentiate or has the line become very blurred?
A universal positive unconditional sentence cannot be true. (This one, for example, is universal, but negative). Here Joachim Sauer is correct.
"A computer without loops is a calculator" is a definition. It cannot be true or false at all. You can accept it or not.
But any definition can be widely or universally accepted or not to be. Or maybe it was sometimes accepted. Here you should choose yourself, what do you want.
As for history, in the middle of the XX century in fantastic literature all computers were called calculators. Later, in 70/80-ties, programmable calculators had hundreds of command places, arrays, cycles, conditional branches, gotos and everything. As I remember, much more programs were made for them than for "large" computers.
Now programmable calculators are a minor business, but they do exist and there are new models of them. Look here.
So, the answers are: no; no(difference is in size mostly); yes, it is blurred. Of course, as far as you take wiki as widely accepted opinion