Larry Selinker (1972) introduced the term Interlanguage (IL) to refer to the intermediate statess ( or interimgrammars ) of learners' language as it moves toward the target L2.
Also unlike L1 acquisition is the strong probability of fossilization for L2 learners- the probability that they will stop their IL development in some respects before they reach target language norms, in spite of continuing L2 input and passage of time.