The spelling "tonne" is only used in countries where there might be ambiguity with the short ton. For the rest of the world, "ton" (abbreviation: t) is the metric ton. Technically it's classified as a "Non-SI unit that is accepted for use with SI," like litres or degrees Celsius.

Source is the official SI brochure: https://www.bipm.org/en/publications/si-brochure/