Yep. An international student is defined as one who doesn't meet the criteria of a home student. If you're on a spousal visa and have been in the UK for less than 3 years, it's very likely you'll be assessed as an international student (from what I've read, at least...more knowledgeable people can correct me/confirm).
Assuming you live in England, the tuition you pay will be identical either way. However, it will affect your student loan eligibility (i.e. you won't be).