In general, any diet that is below 300g of carbohydrates a day is low carb, although the concept is more appropriate to say, under 100g a day is low carb.
Ultra low carb diets are based on the effects of ketosis, a state in which our bodies release ketone bodies that can be measured on ketone test strips. In general, carb intake needs to be around 20g, possibly up to 50g for some individuals, sometimes less than 20g. This low of an intake is often monitored by using the test strips to be sure one is showing the ketone bodies. The benefits of being this low is a significant decrease in appetite, more energy and sense of well being. However, to be this low consistently, it is important to drink plenty of water and be sure to get the healthy fats, quality meats and other low carb veggies and foods. This is not where you have many carbs to play with and the bars, shakes and other processed carbs can easily undo the efforts to stay low. Atkins starts out ketogenic and ups the carbs over time and slowly until you find the number of carbs it takes to lose weight and eventually to maintain weight.
Moderate low carb diets are often easier to sustain for most people. The paleo types rely on eating only whole foods: meats, veggies grown above ground, eggs, nuts, seeds and fruits and honey in limited amounts. Grains, dairy, root veggies, legumes are not eaten. The premise behind it is that IF you can eat it raw as it is grown (without processing), without cooking, it is edible. It is okay to cook the food, the premise is just the help in selecting foods. Dairy is hotly debated, but the principle is that man didn't consume milk until the agricultural stage, when keeping livestock first came into practice. Primal allows dairy.
Common problem area's for low carbers is processed foods, like sugar free products. Commercially prepared low carb versions of high carb foods like tortilla, cookies, breads, etc can keep those cravings alive, even at a lower carb count. Too many low carb desserts can stall weight loss.
I prefer a mixture of paleo and ketogenic. I do go as low in carb count as I can and stay in ketosis most of the time. I do have dairy and wine. I try to stick mostly with whole foods cooked from scratch. However I am also flexible and make the best choices I can with what the circumstances present.
Hope you find the right combination for your successful weight loss journey!
There are many, many types of low carb, the best one is the one that matches your philosophy and eating preferences. If you like convenience foods,