I would define an "encounter" to be an episode of care. For outpatient, this is probably "per DOS". For IP, I'd say "per chart," really as the entire inpatient stay is a single episode of care.
This probably does not help you in the way you intended. I'd advise not ever to conclude or assume anything a consulting or contract company tells you without explicit definition. Follow-up and clarification are usually required.
Keep in mind, that this emerging format of payment (e.g., per encounter, per this or that) resembes what happened to transcriptionists several years back. They went from having base salary and a productivity and quality standard to being paid by line, by character or worse. The overall point here is that companies determining salary on these characteristics signal a bad road ahead. Clearly the professional associations and coders themselves need to do what they can to steer our salaries away from these practices. When the salaries are determined solely on production, quality really begins suffering or being pushed aside to make room for turnover.
Just my expressed concerns. I'd advise all coders to beware of companies playing this payment game.
Kevin B. Shields, RHIT, CPCO, CCS, CPC, COC, CCS-P, CPC-P, CPC-I