The Hadoop in Real World team explains a subtle difference:
cache() and persist() functions are used to cache intermediate results of a RDD or DataFrame or Dataset. You can mark an RDD, DataFrame or Dataset to be persisted using the persist() or cache() methods on it. The first time it is computed in an action, the objects behind the RDD, DataFrame or Dataset on which cache() or persist() is called will be kept in memory or on the configured storage level on the nodes.
That’s the similarity, but click through for the difference.