Core it's the part with amxmodx_mm.dll, modules config files etc. Cstrike addon pack it's the part specyfic only for CS (for DOD, TFC they are different). Just download the files from the locations I posted You links.
To recompile Your custom plugins (these plugins they aren't in core nor in cstrike addon pack) You need to put *.sma files of these plugins into amxmodx\scripting folder, then find the file called compile.exe (in the same folder) and hit "Enter" key on it. It starts to compile all *sma You have in that folder. When the compilation is finished You can find some *.amxx files in amxmodx\scripting\compiled folder - You just need to move them from that folder to amxmodx\plugins folder. That's all the mistery.