A specimen tree is usually the focal point - it's usually large or makes a big impact in some way. Specimen trees are usually too large to be "street trees" - those trees planted between sidewalk and street. Some smaller trees can be treated as specimen trees if they've been trained in some way, or make some other "statement" bringing them in as the focal point of the yard.

An accent tree is just that, something on the sidelines that completes the picture. They're usually smaller or are planted in the background as a screen along a fenceline. Or they "just fit" in some way to complete the overall landscape.

This is all very subjective, and as the seasons change, focus can change from one part of the landscape to another. My fruit trees are mainly accent trees, but in early spring when they're in full bloom they become the focal point. The "real" specimen tree in the yard is a very large elm tree, which shades much of the yard.

You wouldn't want two very large trees planted too close to each other - when they get big, their branches intermingle and they don't hold their shape, since they're bumping into each other. Speicmen trees are usually planted singly so they don't compete with others in the landscape. For example, I have new catalpa tree, but it can't go in the backyard with the elm tree, becuase it would just look bad to have two huge trees competing for my smallish backyard, so it has to go "front-and-center" in the front yard where I currently don't have a specimen of any kind growing. It will also "balance" my front and back yards, each having a large specimen.

Hope that helps - again, it's pretty subjective, but "specimen" usually means big or large or fancy/eye-catching, and "accent" means medium to small or background.