KPO: These are knowledge process outsourcing which helps in outsourcing the critical functions of the business along with information related activities. In other words, you can say it is an extension of one of the business process outsourcing models.
BPO: When companies go out for contracting function, segments and other processes of its business to a third-party provider, that's when you call it BPO process. The two main parts of BPO are front office outsourcing and back-office outsourcing. The operations are already proven and predetermined.