Wolf, et al,
Generally speaking as applied to criminal law:
Statute of limitations: a time period after the commission of an offense during which a defendant must be charged or he cannot be charged at all.
Right to a speedy trial: a limit of time after a defendant is charged when he must be tried or released.
In certain circumstances, the statute of limitations is tolled (paused)such as if the defendant voluntarily left in the state (somewhat more complicated than that, but you get the idea).
The right to a speedy trial is often waived to give the defense more time to prepare.
Note: while you are correct that this aspect of the Sixth Amendment does apply to the states, not every aspect of the Bill of Rights does. (Honestly, who here knew that?)