Switchboard is an official term for gear listed to UL 891 and NEMA PB-2, 5000A max.
Panelboard is an official term for equipment listed to UL 67 and NEMA PB-1, 1200A max. ("distribution panel" is not an officially defined term but I am assuming that's what you mean)
Motor Control Center (MCC) is an official term for equipment listed to UL 845 and NEMA ICS-18, 3000A max., but the first "MCC" as we know them now was made from a modified version of an early version of enclosed Switchboards so there are similarities to this day.
Not asked, but just in case:
Switchgear is not the same as Switchboard and Switchgear is also an official term for equipment listed under UL 1558, NEMA SG-5 and ANSI C37.20
Load Centers are a less expensive version of Panelboards but are built to the same NEMA / UL standards and are not differentiated in the NEC from Panelboards. But Load Centers are generally limited to 200A and use plug-on branch breakers.
If you are outside of North America, these terms might have different meanings (I say that because "distribution panel" (DP) is a term used in Europe more often for what we call a panelboard).
