In the beginning, Maple had indexed names, entered as x[abc]; as early as Maple V Release 4 (mid 1990s), this would display as x_abc. So, x[1] could be used as x₁, a subscripted variable; but assigning a value to x₁ created a table whose name was x. This had, and still has, undesirable side effects. See Table 0 for an illustration in which an indexed variable is assigned a value, and then the name of the concomitant table is also assigned a value. The original indexed name is destroyed by these steps.
 

Assign a value to a subscripted name. The name x1 is now a table entry.
Assign a value to x, the table's name.
Observe the effect on the subscripted name. The name of the table is now "3", and the "subscripted variable" is now corrupted.
Table 0     Assigning values to subscripted variables

At one time this quirk could break commands such as dsolve. I don't know if it still does, but it's a usage that those "in the know" avoid. For other users, this was a problem that cried out for a solution. And Maplesoft did provide such a solution by going nuclear - it invented the Atomic Variable, which subsumed the subscript issue by solving a larger problem.

The larger problem is this: Arbitrary collections of symbols are not necessarily valid Maple names. For example, the expression  is not a valid name, and cannot appear on the left of an assignment operator. Values cannot be assigned to it. The Atomic solution locks such symbols together into a valid name originally called an Atomic Identifier but now called an Atomic Variable. Ah, so then x₁ can be either an indexed name (table entry) or a non-indexed literal name (Atomic Variable). By solving the bigger problem of creating assignable names, Maplesoft solved the smaller problem of subscripts by allowing literal subscripts to be Atomic Variables.

It is only in Maple 2017 that all vestiges of "Identifier" have disappeared, replaced by "Variable" throughout. The earliest appearance I can trace for the Atomic Identifier is in Maple 11, but it might have existed in Maple 10. Since Maple 11, help for the Atomic Identifier is found on the page 

In Maple 17 this help could be obtained by executing help("AtomicIdentifier"). In Maple 2017, a help page for AtomicVariables exists.

In Maple 17, construction of these Atomic things changed, and a setting was introduced to make writing literal subscripts "simpler." With two settings and two outcomes for a "subscripted variable" (either indexed or non-indexed), it might be useful to see the meaning of "simpler," as detailed in the worksheet AfterMath.mw.