These two standards are not necessarily related (bear with me!)...
IEEE 488.1 defines the electrical, mechanical, and funtional workings of the General Purpose Interface Bus (GPIB). This is very much a hardware standard that is full of state machines, hardware addressing, and data transfer protocols.
IEEE 488.2 addresses the limitations in IEEE 488.1. IEEE 488.2 is essentially a firmware specification. It doesn't define how bytes are transferred across the bus (IEEE 488.1), it defines what bytes (standard commands) and how the firmware responds to these byte. For example, if a device receives data bytes that contains a query (command requesting a response) and the host doesn't read the bytes, but instead sends another command, what does the device do with
the response it previously prepared? A 488.1 compliant device (non-488.2 compliant) gets to decide this on it's own (and most of them decide how to do this in different ways!). However, IEEE 488.2 defines precisely how devices communication and dictates that the device generates and error and flushes its output queue in this situation.
In short, 488.1 is HW, 488.2 is SW. 488.2 relies on a bus that emulates the GPIB bus defined in 488.1, but is not restricted to 488.1 implementations. For example, Ethernet and USB both have firmware implementations that follow IEEE 488.2 protocols.