Mate was a funny word; a Kyuubi word, that only Naruto chose to use. Kyuubi spat on the idea of human mates, but Naruto couldn't find a better human word for it.
For Naruto, she was Babe, and he was Bastard. When he felt like teasing, she was Pink, and he ... was still Bastard.
When Kyuubi was predominant, she was Slut, he was Bitch. Kyuubi wasn't very polite.
She was also -- sometimes, never almost, when Kyuubi was sated and gorged on red meat and utterly satisfied -- Mother-of-my-Cubs, and he was The-One-Who-Guards-My-Back. But only in secret. Naruto pretended he didn't know. Didn't share the notions. Wife, Partner.
Vassals. Friends. Skulkmates. Teammates. Fucktoys. Lovers.
Different words, not-quite-meeting notions. Different languages, different impressions.
When they were one, though, there was one Kyuu-and-Naru always agreed on. Both were Mine. No misunderstanding, no nuances, no implications. Because it meant exactly everything they meant, and it was one word that didn't suffer from mistranslation.