The metric system is the same the world over. The modern metric system (known as SI from the French Système international d’unités) is defined and maintained by a number of international organisations.
The definitions are universally accepted for trade and official purposes worldwide. Every named unit has a single definition at any one time.
Compare this with pints, gallons and tons which have different values in the UK and the US!
SI unit definitions have evolved over time to reflect advancements in measurement technology that enable greater accuracy and enable them to relate to more stable physical constants. The values themselves have not changed. It is just that they are more precisely defined. These changes were necessary to meet the needs of high precision scientific and engineering work, and to enable reproduction of the base units using laboratory apparatus rather than rely on copies of physical prototypes. The everyday uses of metric are not affected.
Some conventions remain in common use even though they are not strictly retained by SI. For example, speeds are typically measured in km/h (kilometres per hour) whereas the SI unit is the m/s (metre per second). Nevertheless, the kilometre (being 1 000 m) and hour (being 3 600 seconds) conform to SI in the sense that they are based on the same metre and second.
SI is the arbiter for all other measures
SI is now so well established that non-metric units still in use are actually defined in terms of the metric equivalents. For example, the yard has been defined as exactly 0.9144 m.
UK Metric Association 