As gwassenaar said, in a simplified explanation QAP is Qlik Sense Server without the client (/hub) and a different licensing model (CPU cores instead of tokens). Apart from that they share all the same functionality, QMC, Scheduler, Authorization etc etc
So to install QAP you download the normal Qlik Sense installer, install the product and apply your QAP license key.
QAP is also currently only licensed for external use only and can not be used for internal deployments, that is when Qlik Sense tokens come into play. Note that both QAP and Qlik Sense has the exact same APIs so if you want to build custom internal analytical applications you can do that on Qlik Sense also.