@rockhopper72 I agree the terminology is bad.
Extinction doesn't just apply to sleep training. It means changing any behavior by ignoring it. It's the same thing you're doing when you ignore a tantrum in the grocery store over a candy bar. Sleep training, no matter how you do it, is teaching your child that they fall asleep on their own at bedtime. That's why consistency is so important if you choose to do this. Otherwise you're just confusing them and creating extra stress.
I think if you read any of the many modern books on this topic, like Weissbluth (Healthy sleep habits happy child) they don't tell you to leave your baby all night no matter what. Rather, they often advocate extinction or another method AT BED TIME to start. Night weaning is typically separate from sleep training especially for younger babies. Discontinuing night nursing sessions is absolutely not a requirement of sleep training.
I sleep trained using modified extinction at bedtime, but never night weaned purposefully.
I think the biggest issue with this poor terminology on the internet is that people either think there's nothing they can do and are exhausted for years when their children won't sleep because they don't want to "cry it out" or, on the other side of the spectrum, they leave their 4-month-old alone in their crib all night screaming with a dirty diaper because they misunderstand what sleep training actually entails 99% of the time.
Read a book and talk to your doctor, the internet is crazy and will tell you you're a bad parent no matter what you do.