Losing body fat the safe way does take time – realistically you can only lose around 1-4lbs of fat per week (or around 1% of your total weight per week, according to studies), so if you're losing more than that, then it's not just fat, but it can vary person to person.
Dropping your calories too low will cause your body to go into 'starvation mode', which will actually result in your body clinging onto fat and shedding muscle tissue and water. Carbohydrates are the first macro that people usually drop - thinking they ‘cause weight gain'. Carbs are energy, your main energy source, so don't cut them out completely. Carbs can actually be beneficial to fat loss, but obviously not too many. Adjust your levels to find what's right for you.
You may think cutting out carbs makes sense, but if you cut them out completely, you're cutting a third of your intake (carbs, fats and proteins) so yes, you'll lose weight simply because of the overall calorie drop. However, it's not sustainable, and when you reintroduce carbs you'll then begin to put the fat back on.
Track your progress to find out if you're losing fat, fluid or muscle. Too fast 'weight loss' and you're most likely losing fluid and muscle tissue, with a bit of fat. Losing 'weight' at a reasonable rate means you're more than likely losing mostly body fat, with a bit of muscle and fluid loss.
You will shed some muscle tissue even if you do it the safe way, but you want to lose as little as possible. When someone becomes very overweight/obese they do mainly put on body fat, but they also gain muscle, hence why larger people aren’t usually weak. So it’s only natural that some of that muscle tissue will be lost, but you want the majority of your excess weight loss to be body fat.
Rapid weight loss tends to bring rapid muscle loss too, and also fluid. So be a little patient, focus on your nutrition, training hard in the gym and the results will follow. You will lose body fat at a safe rate, retain muscle tissue, and have a far better looking physique.