Take my linux with me

Dear LQ,

I would like to install linux on a usb stick so that I can work on any computer with my linux and files on it. Most of what I read implied installing a live version of linux and add persistence to it. But I can't help but ask myself : can't I just directly install a (not live) linux on the usb drive like we used to do with hard drives ? would that also work ? if not, why ?

Thanks for your wise words