Larger or smaller. Trip attack or push attack. Fighter

so as a battle Master when it says: if larger or smaller they must make a saving throw or be knocked prone/ pushed away. If they are medium do they need to make this save? 

Is "Medium" larger or smaller than "Large?"

The sizes are:

• Gargantuan
• Huge
• Large
• Medium
• Small
• Tiny

You can find a more detailed description in the DMG.

none of this is answering my question. would they need to roll for a save

"Large or smaller" means creatures of size category large, medium, small, and tiny must make the save.  I Huge or Gargantuan would not make it.

ok thank you