The Short Answer: Transparent vinyl is see-through. Translucent vinyl diffuses light and glows when it's lit from behind.
The difference in translucent vs transparent vinyl comes down to what happens to light: transparent vinyl lets it pass straight through, so you can see the surface behind the decal, while translucent vinyl scatters it, so the graphic glows when lit from behind but you can't see a clear image through it. Choose transparent when the surface should stay visible, and choose translucent when the graphic needs to light up.
At Decals.com, the transparent option is clear decals, printed on 4 mil transparent vinyl. There are two translucent options: translucent adhesive vinyl, which sticks to glass or other clear surfaces, and translucent backlit film, a non-adhesive film for lightbox inserts and backlit displays. All three print in full color. Knowing which one fits your project before you order saves you from reprinting decals that don't match the look you had in mind.