I don't know if they are the same map, but the Guide to Korvosa is really helpful if you are planning to run CotCT.
It allows you to deal with things when your players decide to go in an unexpected direction.
It examines every city district in detail and gives blurbs about points of interest in each. It also has information on Korvosa's history, its day-to-day functioning and its different factions. There's a handy table detailing the various sentences for different crimes that your PCs might commit as well as a listing of common drugs that can be found in the city.
At the end of the book, is a table listing the level and alignment of most important NPCs in the city as well as some tables for random encounters in different sections of Korvosa.
Very highly recommended!
The map is the same in both the Map Folio and the Guide. However, I found the text on the Map Folio a little clearer.
Also, in the Guide the map in bound into the book, so it means you have to cut it out. Even being careful, the edge will never be perfect, if that's a concern for you. It was for me, and I ended up laminating the Map Folio version.
The Guide to Korvosa is important for fleshing out Korvosa like Laric said. It gives a lot of depth to Korvosa. I'd get it.