The 20% is almost always of gross booking revenue, meaning what the guest pays for the nights, before the platform's host fee comes out and usually before cleaning. So on a booking of $500 in nightly charges plus a $120 cleaning fee, a 20% co-host typically takes $100, the platform takes its host service fee off the top, the cleaner gets paid from the cleaning fee, and what's left is yours. Some agreements do include the cleaning fee in the base, which changes that number, so read the fee definition sentence in the agreement rather than the headline percentage.
On the naming: "co-host" is the platform's own word for someone you add to your listing account who can message guests, adjust the calendar, and handle turnovers. "Property manager" is a business relationship, and in a lot of states managing someone else's property for a fee triggers a real estate license requirement. Whether it applies to short-term rental management specifically varies by state, and some states carve it out. So the words describe different things, and the same person can be both.
The thing that catches people at your stage is that 20% doesn't cover much. It usually means messaging, calendar, pricing, and scheduling the cleaner. Supplies, linens, restocking, maintenance calls, snow removal, and the hot tub chemicals are yours. Ask any candidate for a written list of what's excluded and what they charge for a maintenance trip, because that list is where the real cost of the cabin lives.