Type is a standard picklist field on the standard object Event and I want to retrieve the field as I made a modification to the picklist values but I am unable to retrieve it when I retrieve the event object and the when I retrieve it through the field I only get the metadata.
Standard Picklist can retrieved using StandardValueSet so for EventType your package.xml must have an entry like this
<types>
<members>EventType</members>
<name>StandardValueSet</name>
</types>
You can find name for Standard picklist from Salesforce Guide