What is the diffrence between formula field and Rollup summary in Salesforce?

A Rollup Summary field is used to calculate the sum of a fields in the child object record. It is compulsory to be in a Master-Detail relationship to use the rollup summary. A rollup summary field is always created on Master record.(Parent to Child).

Example. You have an Account and multiple Contacts under that Account. Each of the Contact have a number field on it say Contacted People. Now on the Account you can create a Rollup summary to check the Number of Contacted People via all your contacts.

Where else a formula field is mostly used for calculations with in a certain object. And it is child to Parent .