No, the M249 is the SAW (Squad Automatic Weapon). The 240 Bravo is a different animal.
The M249 fires 5.56mm rounds, the 240 is 7.62mm.
The M60 was formerly used in the SAW role, supplanting the BAR in that role. It has also been used on helicopters and ground vehicles as a mounted weapon.
When the M249 was introduced, it was mandated that all M60s in SAW roles be replaced with M249s. The Army went with the M249 originally, and the Marines were also issued them in due course. The Marines quickly figured out that the M249 was a low-power jam-o-matic, and moved on to the M240G.
The M240 was originally intended for vehicular use only. There was an optional kit shipped with each weapon that would allow the vehicle crew to dismount the weapon and use it in a SAW or infantry weapon role. The Marines mounted the kits to M240s and "created" the M240G (for Ground).
FN and the Army eventually figured out that there was a need for an infantry medium machine gun, and developed the M240B, which was purpose designed for infantry use and not a kit slapped on a vehicle gun.