‘To mitigate’ means to make an undesireable thing less severe (literal meaning). Catch-up is better identified as Recovery. To recover means to return to a normal state (also literal). The only slight difference in these two is that recovery means getting back to the condition where no more improvement is desired/needed since you are exactly where you should be. Mitigate, on the other hand, is not necessarily focusing on recovery, rather only on reducing the difference. This is as far as linguistics are concerned. When it comes to planning, the line gets blurred and the focus is on “achieving recovery by means of corrective actions” which have a mitigatory effect on the state of things, but do not stop with mitigatory effects only. While contractors are often asked to mitigate delay, the speaker does not realize he/she is actually asking for recovery because no one would really be happy if the contractor only mitigated the delay …. that would mean the contractor is not actually on track and is still delayed, which is unacceptable, of course. (To make the discussion simpler, I am assuming only normal performance delays without changes or other factors outside contractor’s control).
Acceleration, on the other hand, may be performed even when the project is not delayed. As we know, acceleration is achieved either by Fast Tracking or by Crashing.
Fast Tracking: A schedule compression technique in which activities normally done in sequence are performed in parallel for at least a portion of their duration.
Crashing: A technique used to shorten the activity duration (and thereby the schedule duration … activities on Critical Path) for the least incremental cost by adding resources.
As is obvious, acceleration is a part of Recovery, but is not the only recovery technique.