Can someone clearly explain the difference between the terms of cross-platform and multiplatform?
Cross Platform is where the host development architecture is different than the target execution platform. In short, the target application will not execute on the host development system.
Multi Platform is where a different executable target can be built that will also execute on the host.
Example 1 - You can cross develop from 64 bit linux to 64 Bit Windows using Wine.
Example 2 - You can compile an application for 32 bit Linux using multilib that will execute on 64 bit Linux using the native Linux compiler and using the -m32 switch to build the 32 bit application.
Example 3 - You can target 32 bit Windows applications from Linux 64 if you install Wine32 in addition to Wine and generate both the targets from the same source base if you are using the right toolkits.