A match rod is a float rod, but not all float rods are match rods. I suspect that the lines are getting really blurred now as most matchmen aren't using what would have been called a match rod twenty or thirty years ago. A float rod used in matches these days is probably no more than 12' and quite dissimilar to the rods that are actually called match rods.
If you say match rod to me, it brings to mind what it would have done in the eighties/nineties. A three piece rod, absolute minimum of 12' long, but usually 13' or 14' with the occasional 15'er to be found. The only discrepancy I can think of would be the odd canal match rod which might sneak in at 11 or 11.5' long. Compared to many modern type "commercial" float rods, it would have a relatively fast action rather than a more through action. A match rod might be further split into sub categories of waggler, stick or canal along with appropriate changes in action. A stick rod having the fastest action and canal rod being the softest and most through actioned.