Transfer is digital or physical sharing - if I transfer something to you, you now have some kind of ownership or power over whatever I transferred. E.g., if I transfer some notes to you, you are then able to change what the notes say (or at least on your copy) or a least otherwise have some possession of them.
Assign doesn't need digital or physical sharing. You can be assigned a piece of work to do without ever having any copy of the work. But it does also mean to change ownership.
My guess would be that the contract is covering all possibilities. It's both forbidding giving the agreement away to a third party by any means, either legal or physical. So you can't give someone else a copy without them owning it, but you also can't allow someone else to own it (or otherwise have control over the agreement).