I have a medial plica and it snaps quite nicely under my fingers on flexion/extension even though it is not tender.
Annoyingly, the fat pad scenario is fraught with comorbidities with patellar tendonitis, cruciate tears, meniscus lesion and so forth so just an isolated fat pad might be uncommon:
Duri, Zaid AA, et al. "The fat pad and its relationship to anterior knee pain." The Knee 4.4 (1997): 227-236. The fat pad and its relationship to anterior knee pain - ScienceDirect
Having said that, both those issues can be treated with steroid injection though a fat pad will return which is not surprising given their comorbidities. MRI imaging? beyond my expertise and not readily searchable - maybe someone can comment?