Yes, if you're compiling from source you 'update' by installing the newest Emacs version over top of your old version.
I have installed Emacs from source on my current laptop starting with emacs-25.1.50, and currently I'm running emacs-27.0.50.
When I 'updated' to 27.0.50, I followed the usual compilation steps. The
make install step placed the executable
emacs-27.0.50 in /usr/local/bin, and also created the symlink
/usr/local/bin/emacs -> emacs-27.0.50. So I can open this version of emacs with either
The previous versions of emacs are still in that directory, so I could run emacs 25 via
emacs-25.1.50 - if I was careful to keep the versions of the libraries that I built that emacs with on my system (and assuming no incompatibilities in my config or installed packages). That's only going to be an issue if you are developing packages and want to check compatibility with previous emacs versions. I don't do that, so I've just left the old versions where they are. They take up a tiny bit of disk space, and don't interfere with my current installation.
My answer assumes you previously installed emacs by compiling it from source. If you installed it as a package from the Fedora repository, you should either uninstall that package using the package manager before compiling the version you downloaded directly from GNU; or, just stick with the packaged version and wait for Fedora to add 26.2 to their repository (the difference between 26.1 and 26.2 isn't that big).