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So I have often heard these two in the same sentence. Is it just a fluff thing? Or does their army have any advantages when arming their guys with plasma?

It's entirely fluff based. Well, almost.
The 1st Legion is very slow to incorporate new things and relies on many old systems and relics.
They, by virtue of being the 1st, have access to the oldest gear, which includes plasma weaponry.
The only difference rules-wise is that the Terminators can eqiup Plasma Cannons.

How it came about was the design studio decided that dark angels would be the "relic" chapter, they'd have access to more ancient tech, this was then shown by allowing dark Angel tactical squads to have a plasma cannon, so players (not fluff or the designers) interpreted this as "dark angels love plasma pew pew", this is a popular misconception.

But over the years it slowly creeped in, so when the new book dropped we got plasma on everything, bikes, tanks, land speeders, this is one of the very few cases I can think of that the player base has directly influenced the design and image of an army.