Metering current transformers are designed to be within quite accurate values up to say two x rated current, and down to <0.01 x rated. Consequently a protection relay connected to a metering current transformer will get a heavily saturated waveform during fault conditions and it won't work properly.
IEC Class P CTs for standard IDMT OC or even distance may only be 10% accuracy - it is obviously better of they are more accurate but it is not generally necessary, but the accuracy is at say twenty x rated current.
IEC Class PX CTs for diff applications - we don't care at all about accuracy, just that they are all the same inaccuracy, hence the specification is in terms of physical construction.
Note that connecting a meter to a Protection current transformer will give you some level of accuracy but not for billing purposes. It is also very dangerous as meter devices are generally not rated to handle 20 x rated current for a few seconds.
Having said all that there is nothing "magic" about Metering, P or PX class. They are all copper wire wound around a steel core. They just have different construction to suit accuracy requirements over a range of current values. P class defines the CURRENT accuracy in terms of the allowed connected burden and the maximum fault current. PX defines the TURNS ratio and other factors as the construction specification regardless of the burden.
Use the correct CT for the job and in accordance with local and international standards/codes/regulations/legislation.
Use metering cores for metering and where high precision is required under normal load conditions. For example AVRs, governors, power meters. Use protection current transformers for protection relays and choose the correct accuracy class for the protection application.
There are two reasons that they are called protection and metering current transformers. They are meant to be used the way they were designed for.
I have seen and had to fix many design mistakes using the incorrect class of current transformers.
Example 1: Metering current transformers used for motor protection and metering for a pump house. The pump motors were direct on line started and used to trip on current unbalance when really it was the metering current transformers saturating during the motor starting.
Example 2: Class P current transformers used for generator phase differential protection. The protection relay would trip randomly on differential protection because no two class P current transformers have the same performance/errors as the other. You do not know the knee point voltages, the secondary current transformer resistance, or if the manufacturer has used turns ratio compensation (banned in class PX class).