That’s not quite accurate. Big O notation and Theta notation are different ways of expressing the growth rates of functions - the choice of using Big O or Theta

That’s not quite accurate. Big O notation and Theta notation are different ways of expressing the growth rates of functions - the choice of using Big O or Theta is independent of whether you’re trying to specify total space complexity or auxiliary space complexity. Saying something is O(n) tells you it grows at most linearly, but this would also admit e.g. log n. Saying something is Theta(n) tells you it grows exactly linearly: that is, it is not a slower growth rate like log n, nor a faster growth rate like n^2.