Are these two methods of differential cryptanalysis different?
The approach in the Heys’ tutorial where the author uses the approach

bruteforce last round using every possible keybit [at the output of] active sboxes and trace differentials up to [the output of] $r-1$ rounds

is more fundamental because it is more general.
One needs to meet in the middle at the output of some round and check which value for the guessed keybits results in the highest probability differential for the set of plaintext/ciphertext pairs with a fixed input difference.
It is most convenient and natural to use meet in the middle at the input to the last round, and let the guessed key bits be the bits from the last round.
In fact the other (amazing king) reference is essentially using the same approach (whether the author of the webpage realizes it) since that is a one round cipher with $r=1,$ so $r-1=0,$ and the $r-1$ differential is the input (plaintext) difference.