The centre-half was unsurprisingly the middle position of the 3 half-backs (the line of the midfield 3) in the 2-3-5 formation. It is not the modern equivilent of a centre back at all, it is much more like a central midfielder or rather a defensive midfielder. Anyone using it to indicate the central position of the defensive line, either in the modern game or in the later WM formation is/was doing so incorrectly.
You also said in an earlier post: "No, it's not. A centre-half was a position popular decades a go (Billy Wright was a centre-half for example) that is virtually never played in the modern game. It was much more akin to the modern defensive midfielder, than the modern centre-back."
From Wikipedia Association Football Positions
The position [centre back] was formerly referred to as "centre-half". In the early part of the 20th century, when most teams employed the 2–3–5 formation, the row of three players were called halfbacks. As formations evolved, the central player in this trio (the centre-half), moved into a more defensive position on the field, taking the name of the position with them.
From Conrad Loziak Understanding Soccer Tactics 1966". In 1925 he [Herbert Chapman] converted the attacking centre half [in the 2-3-5] into a defensive player or third back".
In other words, the attacking centre half was moved back to central defence, but retained the name centre half and the number 5. The term centre back was never used back then (at least in England).
I saw Billy Wright. He never played in a position akin to to the modern defensive midfielder. He was the central defender in W-M (2-3-5 was long gone by then) and his job was to mark the opposing centre forward.
Some teams started playing a twin spearhead formation by moving an inside forward up along side the centre forward. To counter this, the other side moved a wing half back into the back line so he was virtually a second centre back, and the formation quickly evolved from W-M to 4-2-4.