Difference Between .rpm and .tar.gz

RPM

Rpm (redhat package manager), is default installation type for all distributions except debian (which use .deb's).
The main uses are
Install from compiled i386|i486|i586|i686.rpm
rpm -ivh applicationname.i386.rpm
this breaks down to -i (install) -v (be verbose) h (hash -- or show progress)

Upgrading comes in the form of
rpm -Uvh appname.i386.rpm
(-U being upgrade)

Rebuilding from a .src.rpm
rpm --rebuild appname.src.rpm
Here the configure and make script are performed automagically. A couple of lines up when the compilation is finished it will say
WROTE: /usr/src/RPM/RPMS/i686/appname.rpm
or something similar. All you need to do then is
rpm -ivh (or Uvh) /usr/src/RPM/RPMS/i686/appname.rpm

Source tar.gz

Most source applications come in tar.gz files. These are compressed files not unlike .zip files. These are uncompressed using
tar xzvf tarfilename.tar.gz
x = extract, z = gzip, v = verbose f=file/force
The sources should now be untarred to their own directory from where you unpacked them.
cd newappdir
(change directory)
run the configure script
./configure
if all goes well, with no errors the make files are now created. Now we run
make
Once all the source files are compiled, the app is installed
make install

The app can now be located in the same dir, or optionally in /usr/bin or /usr/sbin