It may not be clear from the outset whether a proposed arbitrator is entirely impartial since any bias or partiality on his part is only likely to come to light during the course of proceedings. Independence, by contrast, is an objective notion and is capable in many cases of being established or challenged at the appointment stage.
Lack of independence is a pointer towards potential partiality.
It is possible (if unlikely) that an arbitrator may not be entirely independent of both parties as a result of a relationship with one or the other or a connected third party, but may be able to set aside that relationship and come to a decision entirely impartially, based on the facts and the relevant law alone.