I'm attempting to install Apache Tomcat, however i find to various files:

the first is CORE while these guys Deployer

which must i choose?

Download CORE. In the documentation:

the customer Deployer, the industry command spend based script that interacts using the Tomcat Manager but provides additional functionality for example producing and validating web programs in addition to packaging web application into web application resource (WAR) files

The deployer is simply a tool. It doesn't range from the Tomcat server.