No, it isn’t.
Both of them measure different things in the flour.
The Plain flour refers to whether there is anything added into the flour. Such as whether it has nothing added (aka plain flour) or whether there are raising agents added (self-raising flour).
The ‘all purpose’ flour refers to the composition of the flour itself, about the flour’s protein content, milling process, and generally what sort of recipes the flour is suited for.
For example, you can get All-Purpose Plain Flour – which is just straight 100% Wheat flour generally mid-range protein content and suitable for all sorts of recipes.
However, you can also get All-Purpose Self Raising Flour – which is a mid-range protein wheat flour with added raising agents generally suitable for all sorts of recipes.
You can also get Plain Bread Flour – which is 100% Wheat Flour, however it’s generally recommended you use them purely for bread and pizza base recipes due to its higher protein content.
If you’re still unsure, Lighthouse flour explains right on the front of the box what each flour’s intended use is, so there’ll be no more confusion.