You don't need to install both only the commercial version is needed.
If you open a EDU file in the commercial version it will switch to educational mode for as long as you are working on that file. If you then open a commercial file AC will either open it without problems or it will give the warning that it will convert it (prior to AC14 I think) which means that you have to quit AC and reopen it to clear the EDU setting.
If by any reason you are connecting to a TEAMWORk server running EDU the trick that might work is to have a EDU file on your machine, Open AC and select the EDU file then connect to the TW-EDU.
If that does not work, the solution is simple. Change the install folder for the AC EDU version to another folder instead (i.e. Archicad 18 EDU) and once installed you might be able to change the name of the AC executable to Archicad EDU.exe so that you know which one to open.
Remember that you cannot share information between a EDU and a Commercial license by copy/paste, modules, PMK's, etc.
eduardo rolón AIA NCARB Another of the forum moderators. Macbook Pro M1 Max 64GB ram OS X 10.XX latest AC25 US/INT -> AC08