You do pay property taxes even on a condo and sometimes you'll be billed separate for your condo taxes and sometimes the property taxes on the condo will be included in the Condo Association Fees.
Usually the land owner will pay for the main real estate tax although the Condo Owners will be usually billed for the property tax on their Condo in the Condo Association Fees.
I've lived in a few condos where they billed me separately for my property tax on the condo and then another condo had the property tax for my condo billed in with the condo association fees.
Either way though you do end up paying property tax even on the condo someway.