MATE || GNOME = What it is?
Caja || Nautilus = File browser
Pluma || Gedit = Text editor
Eye of MATE || Eye of GNOME = Picture viewer
Atril || Evince = Document viewer
Engrampa || File roller = File extractor
MATE terminal || GNOME Terminal = Terminal emulator
If you don't have aptitude installed, you can get it with
apt-get install aptitude
as root or if you don't want to use it,
alias aptitude=apt-get
If you want to remove GNOME versions, just run
aptitude remove nautilus gedit eom evince file-roller gnome-terminal
as root.
If you want to remove MATE versions, just run
aptitude remove caja mate-text-editor eom atril engrampa mate-terminal
as root.
Own experience with Linux since 2008.