經受 = undergo
suffer = 受難 (or 遭到?) but can also mean 受到(影響) in some cases
Usually it means 受難. but sometimes it can be used to mean something more like undergo (受到影響）, but with a negative connotation (like the previous answerer said).
In the case where it is used to mean something more like "undergo", it is more literary -- so when you hear it in a conversation it almost always means 受難／慘遭。