There is almost no mechanical difference between damage types. Piercing is needed for sneak attack & there are a number of monsters you could probably count on one hand with fingers left over that have some special reaction/treatment of a particular damage type... Other than that, the only meaningful damage type split is nonmagical Bludgeoning, Piercing, & Slashing vrs magical Bludgeoning, Piercing, & Slashing. That boneheaded design choice was a big blow to 5e.Are these legacy traits at all useful mechanically, or are they there so that we understand the narrative behind the weapon?
Asking, because I've considered a subclass that specializes in one of these (as opposed to light, finesse, ranged).
In past editions you had things like a lot of creatures that had dr5/$damageType or dr5/+1 meaning that the first 5 points of any attack you make with a different damage type or weapon that was not at least +1 were nullified so a player would need to weigh the tradeoffs of using their +3 slashing sword of awesome vrs a zombie* with dr5/slash or pull out their not so nice backup slashing weapon (maybe someone's old slash/pierce +1 dagger vrs a greatsword). That had he added benefit of changing how elemental weapons functioned so if Alice had a +1 hevy mace with 1d6 elemental damage attached to it might deal 1d8 bludgeoning and 1d6 fire. That was great at dealing with trash & mook type baddies & remained a good option even if the d8 was subtracting 5 points every attack but against a high AC target Bob with his +3 dagger who was just good at dealing with trash/mook baddies is great at dealing with high AC types. Meanwhile in 5e that flaming mace does 1d8+1 magical bludgeoning and 1d6 fire against everything and is better than bob's +3 dagger in nearly every way against virtually every creature.
Also going in favor of bob's 3.5 dagger is that alice did double damage on a crit & only got a crit on a 20 while bob did doube on a crit if he rolled a 19 or 20. Chuck by contrast might have a rapier or scimitar that does 1d6 damage, crits for double, but crits on an 18-20. Dave's battleaxe i 1d8 & he's really feeling awesome when he rolls a 20 for3x damage & Dave's Heavy pick that does 1d6 crits on a 20 & does 4x crit damage. Those are examples from 3.5's weapons allowed different subjective qualities to make a really magic weapon not as good or differently good than some other magical weapon where in 5e one is objecively better than the other in all ways or entirely unsuitable to someone (ie not heavy, not light, one/two handed rather than two/one handed). 4e weapons also had some of those subjective qualities but the systems are so different that it's more difficult to make simple comparisons
*just an example