I think they are different things. My dad used to run the uk arm/distribution for Compriabnd/Illbruck so would probably know a lot more than me but he seems to be incommunicado (ie out Christmas shopping) at the moment.

Compriband = 'foam' strip to fill gaps springily and flexibly between different materials such as window frame and wood or brick.

Air tight tape - used as specified or designed to seal gaps, usually between either a flexible sheet barrier or larger rigid boards such as OSB. Can also be used between window and wall/other material, but be careful as to how flexible/stretchy it is.

Has this been specified or are you making your own decisions?

Making my own decisions.. which could be unwise!

Compriband (or silicone) as external seal.
Air seal to the internal side (linked to VCL)