The weapon count is only the number of physical weapon shots in a mission. That being every laser, missile, etc. This one usually isn't a limit that you need to worry about since the number of weapons is constantly changing, new weapons are fired, old ones go away or hit their target. The weapon limit isn't anything that should be hit in FRED2, only in an actual gameplay mission. The ships count is the only one that's tied to the mission setup in any way as it comes right from the mission file. Hitting the weapon count meants that at one particular time in a mission that you have the limit number of lasers, missiles and/or countermeasures in use at the same time. But the weapons code will automatically recycle older weapons if it needs room to fire a new weapon.
FRED2 does use all of the same values.
The limits for ships.tbl and weapons.tbl are going to go dynamic with the new pilot code. The network code has been modified to handle more than 130 ships, but those clients/hosts with more than 130 will automatically turn incompatible (temporarily, it's a runtime thing) with retail compatible clients/hosts. This way you can have multiplayer support no matter what your limits are, but it will still be safe for everyone to use too. Other than just being a good thing, this change is mostly so that Inferno can finally have working multi support.