Are "rates" and "a cost" interchangeable in this sentence?
They typically charge for their services, though often at rates cheaper than those the consumer would pay to a private sector procedure.

If so, how the above sentence becomes different?

Question

Are "rates" and "a cost" interchangeable in this sentence?
They typically charge for their services, though often at rates cheaper than those the consumer would pay to a private sector procedure.

If so, how the above sentence becomes different?

Answer

Just expanding a little on Jesse´s excellent answer: Rates often (but not always) refer to longer term contracts (reoccurring payments) whereas costs often (but again, not always) refer to a single, fixed cost.

Answer

Rates is plural, so if you use the word "rates", then that might give the idea that there is more than one rate that this company charges.

A cost is singular, and that would be referring to one specific prices that this company would charge its services at.

So, it just depends on what sort of rate/cost this company is charging. Are there multiple prices that these services come at or is there one specific cost that these services are charged at.