start + (end - start) / 2
Is preferred because there is a possibility in a very large array that the result from (start + end) could cause an integer overflow where the resulting value is larger than the max value for int. This would end up in a negative value, causing the index to be out of the bounds of the array.
it is same, m = (l+r)/2
you should know what it does, In array it takes the array indices and then it find the mid value on its basis we access the mid position's value.
let l = start, r = end, m = mid;
m = l + (r-l)/2 = l + r/2 - l/2 = l/2+r/2 = (l+r)/2.
That's how the fancy formula is straight forward written.
mid = (start + end) / 2 could be done but it is definitely not a recommended way since there could be some cases where starting index i.e  and the last index [n] could be very large. Hence, the value of mid in those cases could overshoot the higher constraint. Hence, to deal with such special cases with much more efficiency and no errors, it is recommended to make use of the following equation to calculate mid value:
mid = start + (end-start)/2
All the Best!!