An actant is a complement of a verb.

An argument is a slot filler of a predicate.

There has been much terminological confusion about the use of the word argument. It originates in predicate calculus and there has the meaning indicated. Roughly since 1975, it has been used to designate ‘actant’, among many other things. On the one hand, liberal use of a term which had a well-defined meaning hampers scientific progress. On the other hand, the concept ‘slot filler of a predicate’ is needed in semantics and has to be distinguished from the concept of the actant since the two concepts are related, but do not coincide.

.Linda forgot John.
.Come in!
.Giorgio se la prende con suo padre.
ItalianGeorge dumped on his father.