ECLIPSE 500 PLT ACKNOWLEDGED CLRNC TO CLIMB AND DID SO. ATC QUERIED THE PLT ABOUT HIS ALT; AND STATED THAT THE CLIMB CLRNC WAS FOR ANOTHER ACFT.

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I WAS CRUISING AS SINGLE PILOT AT FL210 APPROXIMATELY 30 OR SO MILES SOUTH OF RSW VOR AND WAS GIVEN A CLIMB TO FL220 WHICH WOULD CONFORM TO THE CORRECT ALTITUDE FOR MY PRESENT COURSE. I ACKNOWLEDGED CLEARLY TO MIAMI CENTER AND UPON REACHING FL220 THE CONTROLLER QUERIED MY ALTITUDE. I RESPONDED AND HE SAID THAT ALTITUDE WAS NOT FOR ME AND RE-CLEARED ME TO FL180 OR EVEN LOWER WITH A SUBSEQUENT HANDOFF TO THE NEXT CONTROLLER. I STATED THAT I HAD ACKNOWLEDGED THE CLIMB CLEARANCE AND I BELIEVE HE SAID SOMETHING LIKE; 'I AM SURE YOU DID.' THE NEXT CONTROLLER THEN RE-CLEARED ME TO 8500 FT WHICH I ACKNOWLEDGE AND THEN HE CORRECTED HIS CLEARANCE TO MAINTAIN 8000 FT SAYING THAT HE JUST RECOGNIZED THAT I WAS IFR. THIS CONTROLLER DID SAY THAT TAMPA WAS DOWN TO ONE RUNWAY AND EVERYBODY IN THE WORLD WAS COMING TO TAMPA TODAY. TRAFFIC WAS OBVIOUSLY HEAVY AS THEY VECTORED ME CONSIDERABLY MORE WEST THAN NORMAL AND DROPPED ME DOWN MUCH EARLIER THAN NORMAL. NEITHER CONTROLLER SEEMED PERTURBED IN ANY WAY AND ALL PARTIES COMMUNICATED PROFESSIONALLY AND NORMALLY.