BPS is also written as b/s. Both BPS and PPS are used to describe the network bandwidth usage. The relationship between BPS and PPS depends on the packet size. However, the defacto packet size in industry is 64 bytes. To convert PPS to BPS using the formula: BPS = PPS * (64 * 8 ) bits
bps has Kilo bits per second (Kbps), Mega bits per second (Mbps), Giga bits per second (Gbps) and Tera bits per second (Tbps); While pps has Kilo packets per second (Kpps), Maga packets per second (Mpps), Billion packets per second (Bpps) .
The reason why we need pps is that switch/router's packet processing capability depends on packet size. That is, switch/router can't do wire speed for all packets size, but should be able to process most packet sizes at line rate.