Eldritch blast is magic missile.
When TSR first published magic missile back in OD&D, it conjured +1 arrows made of magical force which it then fired, no bow required. It was only later that they were dropped to d4s and auto-hit. This is why they have the +1 damage per die. The number of missiles conjured has also varied from edition to edition. (At various points, such as in Basic D&D, these also orbited the caster until fired like 5e's crown of stars.)
Eldritch blast was created with the Warlock class in 3.5, which at the time was a distillation of the Sorcerer in flavor and mechanics (ultra-limited repertoire, at-will use). At the time, it was a ray -- a ranged touch attack (meaning it ignored armor) -- that dealt scaling d6s (like a Rogue's Sneak Attack, but it scaled to 9d6 instead of 10). This was so the Warlock had an invocation comparable to magic missile that wouldn't break the game by being at-will. It's been since buffed because of its close association to the Warlock making it that class's default attack. (The Cosmic Warlock [Sebastian Crowe's Guide to Drakkenheim] can also make eldritch blasts orbit for illumination and later firing, bringing us full circle.)
They're both just lasers. Arcane lasers. Tasty, tasty arcane lasers. Pew pew.
