You are right about 3-point hitch float--almost none are designed to apply down force. The "other" float has to do with the connection of the lift link to the draft link. On most JD CUTs that connection can be locked on one side so that it acts simply like a pin, or it can be unlocked so that it acts like a pin in a slot. When unlocked, the right draft link can move up and down slightly. This allows the implement to "roll" slightly relative to the tractor in order to better follow ground contour. When using an implement with its own gauge wheels such as a finish mower you want the implement to follow the ground contour of its gauge wheels--not the tractor wheels. The same is true if you are blading snow on a paved surface--you need some roll flexibility between the tractor and the blade to prevent gouging. Roll flexibilty also helps when attaching the draft links to an implement (if you don't have Imatch.)
John Deere has chosen to use the term "lateral float" to describe this slotted connection, but in my opinion it is not a good choice of words. In general, "lateral" means side-to-side, so most people would think "lateral float" means the hitch can move side-to-side. Well it can do that anyway independent of the slot in the right lift link. The lateral motion is allowed by the pivots at the front of the draft links and is limited by either chains or sway bars.
Almost all medium and large sized CUTs have the capability of allowing relative roll motion of the hitch draft arms. Some do it with slots and some use other means. On the other hand, some CUTs do not provide for this at all. An example would be the JD 4100 where it is left off to help reduce cost.
You might want to experiment with using it both ways with your box blade to see if it makes any difference to you in your current leveling task. Leveling with a box blade is an art form. It requires skills that can only be developed with a lot of practice and patience. Techniques and tips have been discussed in hundreds of posts on this board.
Good Luck.
JackIL