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A bps rating often provide the internal bandwidth of the device, often documented for switches. For example, a switch with 48 gig ports requires a fabric of 96 Gbps to allow all ports to transmit at their gig rate, duplex. However, many switch fabrics could be less, for example, I recall many of the original 3750 switch's fabric peaks at 32 Gbps.
Switches and routers need to look at frames and packets and decide what to do with them, and then do it. This is what pps measures, i.e. the maximum number of frames or packets that can be processed. Since both frames and packets often can vary in size, smaller frames/packets require a higher rate to accomplish the same throughput. For minimum size Ethernet, 64 bytes, 10 Mbps Ethernet requires 14,880 pps. However, for 1518 bytes, 10 Mbps only requires 812 pps, much less process demanding.
