Are they spelled “meter” and “liter” or “metre” and “litre”?
Yes. The names of SI units are ordinary words, different in different languages, and sometimes, as in English, they have multiple spellings. (SI unit symbols, on the other hand, are the same in all languages.) In American English, the “-er” spellings are most common, while in British English, the “-re” spellings are used. Both are correct. References: SI Brochure preface • ISO 31-0 §3.2.5 • IEEE/ASTM SI-10 Annex C, §C.5 • NIST SP 811 §C.3.