From my experience the difference is that they delay shipping your item. They claim to have one of the best shipping and handling systems in the world but for some reason they save money by delaying boxing an order for a week, it doesn't really make sense to me. I think they're really just trying to get people to purchase Prime.
I'm sure that there's an aspect of what you say at work, but I can also imagine that they have a certain amount of "pick and pack" capacity at their fulfillment centers.
By choosing 2-day, you're forcing Amazon to pick and pack that order today probably, tomorrow at the very latest.
By choosing "no rush", you allow them flexibility to fulfill from a wide variety of centers, on a wide variety of days. Maybe there's a weekly cycle in order volume and no rush orders may allow them to even that out with a more constant labor force.