The suspended fourth is an alteration of a chord, in which the third is moved up to the fourth note (counting from the root of the chord). For example, in
Csus4 the third is moved up to the f. In the classical harmony the fourth has to be resolved to the third. In jazz and pop a lot of times this chord will be followed by a regular triad as well. (Though in some styles the
sus4 sounds fine as it is.)
In sum, the
sus4 is a third that is moved up and probably will move down. Thus, this alteration is a suspended third. I always thought it is kind of strange that the alteration is called
sus4. To be exact,
sus3 would be more correct, or simply
4. But, that is the way it goes in languages; it’s not a rational process and sometimes strange terminology arises.
If there ever would be made a standard for writing chords, I would prefer the indication
4 for this alteration. It’s short and cannot be confused with another alteration or extensions.