The problem is that there is no one definition of "low carb". Some people consider under 150 g/day low carb, but I don't.
Before "keto" came along many of us were what I consider "very low carb" (and you still might see that around as "VLC") In my head that's about 20 g of carb a day and then there's even debate as to whether it's net or total carbs. I consider up to 50 g. of carbs as "low carb" and beyond that, reduced carbs compared to the SAD. But that's just my own personal opinion. There's no authority for any of this.
Keto I think is somewhat fluid, too. What people used to call VLC is most definitely keto, but as you point out, some people can be in ketosis on 50 g of carb, so I would say the aim of "keto" in particular is to show positive ketones on urine, breath, or blood meters, while that's not the stated goal of LCHF (even if it is often achieved on LCHF).
IMHO, LCHF with very low carbs and keto are interchangeable as long as you are showing ketones. It's also possible to be LCHF with very low carbs and NOT be in ketosis. Personally I didn't see any big difference in weight maintenance between very LCHF with measurable ketones and without measurable ketones, so I'm more along the lines of LCHF. But they are so close I don't worry much about the distinctions between them. "Keto" is cool and it seems more acceptable to males for some reason--perhaps because the general public doesn't associate it with "that Atkins Diet" that nearly every woman in the western world has tried at one point in time (fFWIW, Atkins induction is no different that VLC, strict LCHF, and keto IMHO).
Totally in my own mind and probably not many others, I like to see keto as the love child of Paleo and LCHF (and grandchild of intermittent fasting while we are being nepotistic). It's low carb and Paleo-style clean eating. But I get that others don't see it that way and will eat very low carb stuff that's never going to be considered Paleo if it works for their production of ketones .