Typically, a P&ID diagram would not show specific electrical devices such as the motor starter itself; it would show the machine the starter is connected to, even if it does show the H-O-A switch. That's because the H-O-A is a control point, something that would be pertinent to the process flow. How it happens, i.e. the starter, is somewhat irrelevant.
What is the symbol? If it is a valve or actuator, SSD could mean anything, i.e. Secondary Sludge Digester or Steam Supply Diverter. If it is a plain box, it might mean Solid State Drive or possibly Soft Start Device, but I doubt it, because again, a soft starter is just a starter, the finer points of how it does its job is irrelevant to a P&ID diagram.
But the real answer is, only the P&ID drawing legend will state for sure what it means. There is no "standard" per se.