We report a new free-floating planet (FFP) candidate, KMT-2017-BLG-2820, with Einstein radius θE ; 6 μas, lens-source relative proper motion μrel~8 mas yr？1, and Einstein timescale tE = 6.5 hr. It is the third FFP candidate found in an ongoing study of giant-source finite-source point-lens (FSPL) events in the KMTNet database and the sixth FSPL FFP candidate overall. We find no significant evidence for a host. Based on their timescale distributions and detection rates, we argue that five of these six FSPL FFP candidates are drawn from the same population as the six point-source point-lens (PSPL) FFP candidates found by Mroz et al. in the OGLE-IV database. The θE distribution of the FSPL FFPs implies that they are either sub-Jovian planets in the bulge or super- Earths in the disk. However, the apparent “Einstein desert” (10 <θE/μas< 30) would argue for the latter. Whether each of the 12 (six FSPL and six PSPL) FFP candidates is truly an FFP or simply a very wide-separation planet can be determined at first adaptive optics (AO) light on 30 m telescopes, and earlier for some. If the latter, a second epoch of AO observations could measure the projected planet？host separation with a precision of？(10 au). At the present time, the balance of evidence favors the unbound-planet hypothesis.