Difference Between Reported Distance and Administrative Distance

Reported Distance is the distance (metric) towards a destination as advertised by an upstream neighbour. Reported distance is the distance reported in the queries, the replies and the updates.
Reported Distance → The total path between a router and the next closest router.

Admistrative Distance is a measure of the trustworthiness of the source of the routing information.

Difference between Metric and Administrative Distance ?

Administrative Distance determines what priority will be given to each Routing protocol redirected through a router.
Metric is a Calculation done by the Routing protocol to determine the best path through a network.