string trimmers vs. blade trimmers
Blade trimmers (for weed and grass cutting) work with blades instead of the monofilament string used by string trimmers. They are much less common than string units, and like these are used for trimming tasks along walks and flower beds or in places too irregular or narrow for lawnmowers.
Some blade trimmers can also use nylon strings. In this case, they have a higher torque to turn.
Blade vs. String trimmers
The reason of the idea of using sharp metal blades instead of monofilament string is easy to devise: very tough weeds can cause the string trimmer engines to stall or bogging down, or strings to break very often.
But blade trimmers have an obvious and major drawback: the risk of injuries. In fact, the contact of the blades with the ground can be very dangerous. Contact with hidden or unexpected objects like rocks can cause major injuries... Only in well manicured and kept lawns the risk disappears.
On the other hand, string trimmers cope well with hidden rocks and obstacles, and are particularly safe. They have evolved and became popular exactly due to it, and to their effectiveness - that makes them, in most cases, a much better solution than blade trimmers... See: Electric vs. Gas String Trimmers
See also:
Hedge and lawn trimmers
String vs. Blade Trimmers
Hedge and grass trimming shears
The best of lawn and string trimmers