What's the difference between accede and acquiesce, don't they mean the same thing?

Accede is a synonym of acquiesce.

Acquiesce is a synonym of accede.

As verbs the difference between acquiesce and accede is that acquiesce is to rest satisfied, or apparently satisfied, or to rest without opposition and discontent (usually implying previous opposition or discontent); to accept or consent by silence or by omitting to object; — followed by "in", sometimes also by "with" and "to" while accede is (archaic|intransitive) to approach; to arrive, to come forward.