The difference is that partial recursive functions are partial functions. A partial function f:A⇀ B (note the special arrow!) is a function that is, in fact, a function f:S→B where the domain S is a subset of A. For all values in A∖S we have that f is undefined. If S=A we say that the function is a total function.
a primitive recursive function is a partial function.
Source : https://www.quora.com/What-is-the-difference-between-recursive-functions-and-partial-recursive-functions
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