While I cannot say that my answer is from the standpoint of an authority, as I'm not really an authority, I can share what I think about the weightloss vs recomposition problem.
Most people say they want to lose weight, when in fact they just want to look good naked. To an unexperienced person, weight loss = fat loss = looking good naked. So they ask "How do I lose weight?" instead of "What should I do to look good naked?". It's a form of the popular XY problem.
Body recomposition is about decreasing your body fat percentage while maintaining or even gaining muscle mass. It's hard to lose fat and gain muscles at the same time (usually only possible for beginners), so most of such programs have phases- the so called bulking phase (gaining muscle mass) and cutting phase (losing fat). The phases differ in diet and training program.
IF you want to look good naked, you WILL need to have those muscles. If so, why waste the ones you already got, and lose them in the process of a typical weight loss program (lots of cardio done on a acute calorie restriction), if you could work towards your goal from the beginning?
On the other hand, there are people who might want to just lose weight. Those would be people morbidly obese - their goal is to actually lose weight, because it impairs their normal functioning. They simply want to get smaller, and they don't really care if they lose some muscle mass in the process. They will probably be losing connective tissue along the way too, since when there is less of a body to support, they wont need as much of it.
In both cases, the baseline is the diet. Actually, a good body recomposition diet will work well for the weight loss goal, so I don't think there is a lot to be said about it in this answer: just remember to eat enough protein and bear in mind that diet is 80% of your success. I personally like the low-carb diets.
With diet out of the way, we can go on to the training program.
A typical body recomposition program will include some form of resistance training, for example weight lifting, perhaps with elements of cardio (I'm not a fan of cardio exercises, and I personally recommend weightlifting and high intensity interval training).
A training program for a person trying to simply lose weight could be pretty much anything that person fancies,but most instructors recommend lots and lots of cardio.
If you're just trying to lose weight, probably your own bodyweight is enough challenge for you, and you should not burden yourself and your joints and muscles with additional iron. Can you imagine a person as wide as she/he is high, doing squats with a 50kg barbell? Doing interval sprints, while walking up the stairs is a problem for them? Me neither. In the morbidly obese section, pretty much any exercise will help, especially that diet is still most important factor.
After some time and losing enough weight, a weightloss person will probably change his/hers goals and will want to go for a body recomposition, modify their diet accordingly and pick up on a proper workout schedule.