Bandwidth: measures the volume of data a network can transport per second, (Link Capacity, Max Capacity of network link to transfer data over time)
PPS (Packets Per Second): measures the processing rate of network hardware handling individual units of data. (Hardware Capacity- router max processing speed)
The Relationship and Packet Size PPS is entirely dependent on packet size. A 1 Gbps connection can be filled by a few massive packets or millions of tiny ones. Network devices (routers, firewalls) have to read the header of every single packet to figure out where to send it.
Because of this, processing 1 Gigabit of 64-byte packets requires vastly more CPU power than processing 1 Gigabit of 1500-byte packets.
The basic relationship is:
$$PPS = \frac{\text{Bandwidth (in bps)}}{\text{Packet Size (in bits)}}$$
_(Note: Real-world calculations must account for Ethernet overhead, typically 20 bytes per packet: 8 bytes for preamble + 12 bytes inter-packet gap).