The meaning of the $\alpha$ helix and $\beta$ sheets in proteins
The answer is very simple. As described in the accepted answer to the related question about alpha-subunits vs alpha-helices the alpha- and beta- are arbitrary names. It could easily have been 1 and 2 or A and B based on ordering of letters or numbers; indeed, there are &quot;type I&quot; and &quot;type II&quot; turns.
The history, from the wikipedia page on alpha-helices says:

In the early 1930s, ... William Astbury initially proposed a kinked-chain structure for the fibers. He later joined other researchers (notably the American chemist Maurice Huggins) in proposing that:

The unstretched protein molecules formed a helix (which he called the α-form)
The stretching caused the helix to uncoil, forming an extended state (which he called the β-form).


(Emphasis added). In other words, he named the &quot;α-form&quot; first, and considered the &quot;β-form&quot; to be an uncoiled form of the first one. These names later became &quot;α-helix&quot; and &quot;β-sheet&quot;. It could easily have been the other way around.
Indeed there are other types of helix; the 310 helix and the π-helix. If either of these had been discovered first, perhaps they would be the alpha-helix. Of them all, the 310 helix has the most 'logical' name as:

the helix has three residues per turn, and ... has 10 atoms in the ring formed by making the hydrogen bond

so if we followed a similar naming scheme, the alpha helix would be a 3.613 helix. Admittedly this is a bit of a cumbersome name.
As well there are the alpha sheet - a sheet made of helical strands - and the beta helix - a helix made of strands. For both of these, the &quot;alpha&quot; and &quot;beta&quot; part of the name has been chosen because of the naming of the original structures they are related to.