remove […] puts the ‘removed’ elements at the beginning of the sequence
What? No. Both remove_if and partition put the “good” elements first. partition puts the “bad” elements after that, whereas remove_if does not specify what comes after it — it might be the bad elements, but it might also be copies of any (either good or bad) elements.
For example, if you partition 1 2 3 4 5 on even, you might get 2 4 5 3 1 (note that each element occurs exactly once), whereas if you remove_if the odd elements, you might get 2 4 3 4 5 (note the duplicates).