Iirc the signal de botrange is 694m high, the staircase is 6m high so you get to 700m. Although it doesn't look 6m high on the picture. I've only been there once as a kid, so might not be accurate.
Yes, both are in the nature park "high fens", it's less than an hour walking between the 2. Baraque Michel is about on the edge of the park, Signal de Botrange is somewhere in the middle. The High Fens is pretty flat, so even though it's a few km away, there's not that much height difference between the 2.