"Metering" vs "measuring"

It seems that

Measuring is mostly used to ascertain the dimensions, quantity, or capacity of something and Metering is mostly used in supplying a given amount of something using a meter which according to the free dictionary is

Any of various devices designed to measure time, distance, speed, or intensity or indicate and record or regulate the amount or volume, as of the flow of a gas or an electric current.

But as mentioned by Peter, the metering can be measuring the supply too

Metering associates with the continuos flow of a commodity or product that and is difficult to batch measure. At the point of use, electricity, natural gas, and water are continuously metered and totalized. The total amount used within a period of time, usually a month, is then multiplied by the commodity charge plus a tariff for the some or all of the local, state and federal governments. The dispension of gasoline and diesel fuel oils are another example of metering.

Measuring associates with the dispensing of a proucuct in a single batch. When one orders at the deli counter, the products are dispensed by weight which is measured. Also, most of the packaged food products purchased at a supermarket are premeasured either by weight or volume. A cup of coffee is another product that is measured and not metered.

Metering is data acquisition that is read directly from the interface. Hence there's meter reading proof.

Measuring is data acquisition that is read indirectly from the interface. Indirectly means the interface provides indicative value for further data processing method or algorithm. Hence there's only indicator proofs available.