HOA Management Company Services

I am a bit confused on the different services offered by a collection of management companies. I've researched a couple of management companies, and I've found that generally they break their services up into three categories:

1. Administrative - Includes duties such as meeting records, 24 hour emergency services, CC&R enforcement, dealing with vendors, insurance, etc.
2. Maintenance - Includes duties such as site inspections, contractor bids, etc.
3. Financial - Includes duties such as budget preparation, assessments, accounting, financial statements, reserve studies, etc.

I've also done general research (through this site and others) and found that management services are often broken up into a three-level hierarchy of responsibility:
Financial-Only Management
Full Management
On-Site Management

My question then is what exactly constitutes Financial, Full, and On-Site management? Which services could be expected of each category? If I selected On-Site management services, how would that be different than Full management? How are the first three categories (Administrative, Maintenance, and Financial) broken up into the second three (Financial, Full, On-Site)? What exactly should I be expecting from my management company?

*NOTE* I think the financial categories are pretty self-explanatory, and am mostly concerned with the others.

SaraM, some HOAs only want accounting services while other HOAs chose full (total) services. On Site means the Manager lives on the premises. Your HOA can determine what management services are desired and write an Agreement for just those services. Attached is an example Management Agreement our company uses.