Cunningham's formula is a pretty good formula to estimate RMR, especially in athletes
RMR = 370 + 21.6 * FFM
FFM is fat free mass, as you might expect. Many online sites just use other formulas, or deduce your FFM from your total weight and height using for example your BMI (weight/height^2) and Deurenberg's formula.
So, it depends. If a site is asking you for your weight and not your fat free mass (which is usually what people have handy), it is likely asking for your weight and using some heuristic as the one I've shown above.
If you are training and have access to your FFM via a DEXA scan for example, you can calculate that using the formula directly and don't need any site to calculate it.
A final very important point is that this number is not really important as you should take it only as a starting point to achieve your goals.
Then you should measure your progress and adjust your intake based on your progress. For example, you've determined you expend 2300 kcals daily based on your RMR, your activity multiplier, your training expenditure, and your food thermogenesis.
Then you try eating just 2300 kcals if you want to maintain, about 10% more than that if you want to gain or about 10% less than that if you want to lose. Do it for some time (1 or 2 weeks) and measure. If your measurements are consistent with your goals (maintaining, gaining, or losing), it means the numbers were calculated properly for you. If the measurements don't match, ADJUST the TARGET by another 5 to 10% and measure again in one or two weeks.
This method does two things:
1.- It avoids making you have to go periodically back for a heuristic that may or may not match your body.
2.- It is perfectly matched to your circumstances and reality. So if you gain a lot of muscle, for example, you'll be able to adapt your target automatically.