This is a broader category; Jessner's is a specific clinical presentation of a benign lymphocytic infiltrate, characterized by non-scaly, annular plaques on the head, neck and back.
A true lymphoma is distinguished by being a monoclonal proliferation on biopsy, whereas Jessner's is a polyclonal (benign) infiltrate.
Clinically and histologically very similar (or identical), it is distinguished by some experts by its marked photosensitivity, a feature not required for Jessner's.
PLE is a transient, itchy eruption that appears acutely after sun exposure and resolves, unlike the persistent, non-pruritic plaques of Jessner's.