I take it you refer to Pressure Relief Valves (safety/relief valves). In which case, an oversized PRV chatters because the capacity of fluid being relieved is too small to keep the valve properly open. Hence the valve relieves a small amount and slams shut again, then repeated many, many times (like a piston engine). A properly sized/selected valve will have a maintained rate of flow which allows the valve to open fully and more stable. As the pressure decays in the vessel the valve closes at a point below the set pressure. The closing is referred to as blowdown.
Per ISO-4126, only the term Safety Valve is used regardless of application or design.
I will also add that chatter is more likely where the fluid is of non compressible nature, ie., liquid. Also, chatter is caused by various other factors or a combination of them. Besides an oversized PRV, chatter can be caused by long inlet piping causing inlet pressure drops, inlet piping that has flow diameter smaller than the PRV inlet size, high back pressure, varying flow rates, incorrect installation, etc., etc,. Also the design of PRV used affects performance. a modulating pilot operated pressure relief valve can be a solution. but not always. Most common PRV chatter is caused by oversized PRV selections and inlet pressure drops.
PS: I future, Please post PRV related questions in the specifica Safety/Relief Valve Forum. Thanks.
Per ISO-4126, only the term Safety Valve is used regardless of application or design.