Basically the same thing.
Mmm... somewhat. Keto by definition is very low carb (<20g/day), while low carb is typically 20-60g/day-ish and treats the metabolic pathways a little different. I get my sufficient satiety via protein intake; after about two weeks the stomach resizes itself so the "lack of volume" aspect is only an issue at startup.
But, hey, if it's working for you -- keep it up! I'm losing 1 lb/week atm, and eat both girl scout cookies and bacon daily. Meh.
And you're probably aware of it but I think it bears repeating -- be mindful of when you get off of the diet. Don't go back to your old lifestyle, else you'll just go back to being fat. Total caloric intake trumps other aspects, so it's good to have that concreted. Unless you plan on doing this forever, "eat until you're full" is a very bad habit to pick up.
you get a calorie deficit of about 1000-1500 kcal/day.
Is something I don't approve of on the fundamental level, at least pending the initial weight of the individual. I can appreciate finally being eager to get thinner, but at deficits that large the likelihood of LBM loss (metabolism loss) and loose skin is higher. I'd rather pull a tortoise via methodical approach while maintaining my metabolism. Fun side note -- two years ago I needed 1800 cals/day to lose weight. I bulked up a little last year, and with identical activity levels I'm seeing the same results at 2000 cals/day. More LBM is awesome.