Just to catch everyone reading up to a common place, here is some literature:
Liskov's (2001) Program Development in Java describes a total procedure as total if ..."its behavior is specified for all legal inputs," (54). A partial, then (as she also writes), is partial if illegal input is allowed and the behavior for that input undefined.
Though a few subtleties are not explained above, the distinction from my own research between total and partial appears pretty distinct, particularly for statically typed languages. From my understanding, the term "partial" is most often used to refer to the allowance of breaking formal parameters to procedures - arguments that cause an unhandled error within the body of the procedure.
Are procedures written in a dynamically typed language - here for primitive inputs - partial or total?
If you've got the book, another page to look at carefully is p. 58 (if not, you can find a pretty solid pdf of it online, somewhere).
Note (concerning comments):
I understand the notions of partial and total are language independent and refer specifically to each procedure;'s implementation; however, I am asking this about dynamically-typed languages in general where "legality" of input - and the enforcement of those rules - appears to be less well defined