Chrome Extension vs. software installation

I've been using  teamviewer for years on my windows computer. I typically download and install the softare on each box and log in to my account. I'm now plan on transitioning over to chromebooks.  I cannot find any documentation concerning what the difference is between the "teamviewer extension in chrome"   vs. actual installation of the teamviewer software on the computer. 

Can anyone "enlighten" me on what the extension brings to the table? .... With the latest updates in chrome OS, i could install the software on the chromebook if necessary. but if not, i'd rather keep thing as simple as possible on this device. I just cant find anything that differentiats these two products. Will adding the teamviwer extension to chrome  allow me to connect to my other teamviewer installations? will i be able to connect to this chromebook from my other installations with just the teamviewer extension loaded in chrome?

thanks in advance for any knowledge or recommendations

Greygoose