Traditionally, a “free” safety played on the opposite side of the field then the tight end lined up. With complex offenses that move around weapons constantly, the discrimination between free and strong safety is very blurry. It is best to say that a free safety is one who’s talents tilt more toward coverage and playing away from the line of scrimmage.
The strong safety traditionally means a safety that lines up on the same side of the field as the tight end, but with the way offenses are moving weapons all around, it really just means a more physical safety that is strong against the run and that can be effective close to the line of scrimmage. Some teams have found amazing athletes that can play the strong safety position and that can move all over the field. This super-versatile position is very difficult to find, as you need a player that can cover in space, tackle, move sideline to sideline effectively, cover tight ends, blitz, cover centerfield, and have strong recognition skills. There are a few in the NFL now, and one or two each year in the draft.