Both have the same actual coupling mechanisn and same actuators.
The main difference is that the old-FD lenses have a bayonet breech-lock ring, that one has to twist for locking. (Actually with most lenses it twists itself a bit at mounting, thus keeps itself from falling off at least, but needs to be tightened.)
With the new-FD lenses one has to twist the whole barrel for locking. (The actual mounting face remains steady unseen meanwhile). Thus this is a "true" bayonet mount in the common sense.
Some photographers find the new-FD lenses more practical. As with the old-FD ones one first must be shure that the breech-lock ring is at the "open" position at first. (No issue if correctly taken off before). Secondly at not correctly aligning a prematurely self twisting breech-lock ring may irritate uninitiated users.
Anyone accustomed to the old-FD mount should be able to use it without hick-ups
The new-FD mount, due to its complexity at the mounting face, can cause real trouble, as the lens getting stuck for good at the body, if a tiny grain of sand gets onto the wrong place. Nothing to be solved at location.
The locking mechanisn itself of the R- and FL-mount lenses is the same as with the FD lenses, though both differ in actuators.