True, a Caspian Tern has a slightly forked tail, but Common Terns have deeply forked tails - almost as much as a Barn Swallow. In straight flight like this, it would appear deeply forked. It looks much less forked when they fan their tail for turning, hovering, etc. (The tail shape isn't always as obvious when they're perched.)
The two quickest ways to separate them in the field are by voice (I usually hear them before I see them), and flight style.
BB