We want you to use the right weapon for the situation, so we’re avoiding systems that encourage you to use the same weapon over and over again to improve (although of course, using a weapon a lot may increase your own player skill…).
With this in mind, XP is not specific and you can use it to spend your way through the progression trees. There are plenty of accessories to unlock as well as weapon specializations that increase the efficiency of using weapon types.
In addition, there are randomized loot rewards with a different currency set for specific weapon bases and upgrades. However, this doesn’t mean that if you want to use a Plasma Gun you have to wait for it to randomly pop up – you can always predictably purchase the base version of a weapon type from a vendor!