A lot of these websites have the wrong information loaded on them

Normally they state that the 16% tax is applicable if you are exempt from it as you define and the city/local tax field is populated with seguro hotelero which is normally about COP7000 pppn give or take a couple of thousand. That is an optional tax and I have not worked out what it is for but lots of places say it is not payable if you have travel insurance

My guess is that the hotel owner above has mentioned in one field that there is a 16% sales tax if you are not exempt and then added it again to the city/local tax field. It is a Colombian hotel trying to apply their own costs to a website based on a US model. For example somewhere like Honolulu there is a state sales tax and an additional city tax. They have just added the same tax twice by the looks of it

I would not worry about being charged two taxes. If it says that tax is not included at all and you are exempt from it as a tourist then so be it, you will not be asked to pay an additional city tax. No cities in Colombia have city taxes.

Some properties in national parks have an obligatory contribución al turismo. The nearest place to Cartagena with this charge is the Islas del Rosario, and unless you are staying somewhere like San Pedro de Majagua or Gente de Mar resorts then you will not have to pay it.

Have a great visit