BPS (Business Process Services) is the Product of a BPO company..
A simple analogy to illustrate it --
Apple (company): iPhone
Paychex (company): Payroll services
BPO company: Business Process services
Some example of services (BPS) offered by BPO's:
1. Back-office support
-- Data processing
-- Chat and E-mail support
2. Call centers
-- Customer Service
There are other elements and variables involved in between, this should give you an overview.