What is the difference between user mode and privileged mode on a Cisco router?

User Mode: for view some of little configuration

Privileged Mode: for allowing administrators to configure cisco device

Usermode: limited to an array of show commands, basic reachability tests, such as ping and traceroute, as well as other ways of viewing configurations and status info of a Cisco device without the ability to make changes.

Privileged mode:  is for users that have been delegated admin privileges and need to make changes, view more show commands and debugs as well as using the ability to move further down the configuration hierarchy (such as global configuration mode, interface configuration mode, etc)

I think the major difference is that you can ping other devices from privileged mode but you cannot do that from user-mode.

User mode is used to just view the configurations of the router and Privileged mode is used to view all configurations on the router and also allow to change some less important configuration.