So most of what I see about a library economy is that you can use items indefinitely, and I absolutely think that we should have that ability. The actual mechanism of how it works is up in the air, and hasn't been deeply explored to my knowledge. What I imagine is that people say "I need this for x time" and it gets catalogued. If someone tries to check out a luxury item (imagine like a book or something) after the due date, they must return the other item first or has the option to extend the borrowing term as far as needed. Things that would be essential would still be available, but the person gets reminded about their obligation to the community to have the item returned.

As for how it's different, an everything library can exist in some capacity in all systems. The difference is that a library economy allows for items to be used without cost, and doesn't commoditize the items. It creates a system of mutual respect towards the rest of the community, and incentivizes groups of people to act creatively together for projects. It functions more like a store where you don't buy anything and return it to the community, rather than paying money to use a tool for a week. It also incentivizes highly durable, extremely usable objects (imagine the right to repair, but without any anticonsumer behavior)