Why does the request status say In Progress, but the activity status is Approved?

If the request status is In Progress then it is still awaiting approval from at least one approver for at least one workflow step.

In this instance, the Activity may be approved, however,  one or more Recipient(s) may still require Approval. 

Status of each recipient is shown in the approval flow. A detailed view of the defined approval flow for the request can be found by clicking on the Request Status located in the Request Details box. 

 Click here for more information on the Approval Flow. 

Click here for more information on Request, Activity and Recipient Statuses