There is no difference as far as the NEC and UL are concerned.
For the most part loadcenters are cost reduced panelboards targeted to the residential market. However, some manufacturers offer multiple lines of loadcenters and paneboards so there is no single clear difference. While very few loadcenters accept bolt-on breakers, there are many panelboards that accept plug-on ones.
Some common differences are:
Loadcenters
14-1/2 wide x 3-1/2" deep box to fit into stud space
Lots of knockouts for cable entrance
Limited number of options in enclosure type, NEMA 1, 3R, and semiflush
Covers are often dual surface/flush mounted
Panelboards
20" wide x 5-3/4 deep boxes allows more room for conduit entry
Few knockouts, maybe even blank end walls.
Enclosure options may include NEMA 12 and NEMA 4
Covers may be available with two sets of hinges (door-in-door).