Difference between rpm -ivh <package> and yum install <package>

For rpm you must specify where to get the file with the new version of the package.

yum, which is a more intelligent management system, try to find a new version of the package in their repositories, will look for the package dependencies, will look for the fastest repository mirror (and make a lot of other pleasantrie)

• rpm - RPM Package Manager.
• yum - is an interactive, rpm based, package manager.

there is no difference if you're installing single file as both yum which is wrapper for rpm and they both offers same core functionality, however yum can do more as yum works with repo(s) and it can handle updates & has plugins, while rpm works with file(s).