I agree that fat loss and weight loss are often used to mean the same even though we, as professionals, understand the difference.
Particularly when dealing with women, though, there is another powerful way to communicate that concept which is dress size. It is not coincidence that so many ads will feature somebody saying: “I went from a size 18 to a size 8.” It is a bit more tangible.
Fat loss in particular, while more accurate, is difficult for a layperson to relate to. We can measure it with body composition but the client by him/herself can only see numbers as in weight, dress size and inches.
Fat loss is much preferred to weight loss technically, but your clients will refer to it as fat loss. Almost everyone assumes that when people are talking about weight loss they are talking about fat loss. So technically it’s a big deal, but in daily usage I think professionals and clients/potential clients are on the same page in meaning… It could help your marketing stand out though if you were to say “fat loss” because it’s a little different from what others say.