Well... yeah, it does but not exactly, at least not always exactly.

Hard to explain, let me try though.

всё ещё is just still, just to indicate that the action is not yet stopped.
всё также might add a different shade of meaning, noting that the action is not only continuing but also is as good, strong, intense as before.

That's why I said:

or more precisely as before
I think the expression gets this additional shade because of the word "также", which can often mean "same".

But there is a very thin line between "всё ещё" and "всё также". Sometimes they can mean exactly the same, even coming from native speakers.

P.S. Just to further boggle your mind, joking:

Кирилл, всё ещё занимаешься боксом? - I'd say that if I thought Kirill didn't have the stomach to continue on with his boxing training. I could have added a sarcastic tone as well. Or I could just say that if I wasn't sure he is still taking boxing lessons.
Кирилл, всё также занимаешься боксом? - I'd say that if I was expecting him to still be working on his boxing.

Cheers