Not sure this even matters but I have too much time on my hands waiting for parts to arrive. I've been describing my machine axis as in the pic (movement on gantry is Y) but most folks and software default to opposite. I started to notice it when watching CNC tutorials, autocad UCS always defaulted to side view as x but it's just a relative reference, using metric in the US for example has been a real mess for ordering machining and mechanical parts, (what year is this 1966?) I'm sure gcode doesn't care but might want to change my mindset to avoid confusion when seeking help.
This has been discussed in several other threads throughout the forum (here for example) but basically you are viewing it from the wrong angle. Traditionally when you stand in front of a machine, x goes across, z goes up and down, and y moves front to back. The side rails are just that, 'side' rails so if you are facing the side rails you aren't at the front of the machine.
All real interesting but still odd, but have to admit it must be the standard. I wouldn't ever intentionally stand in front of a machine or gun and you never "face" an axis in measurement, always from the side. Though chips fly 360° it just looks more threatening. Operator station is usually on the longest side except with a cube, something about the length of a human arm. I always looked at it from the perspective of how math is taught, first is 1D x and longest should be fixed ... but I have seen the light and will join the crowd.
I have always assumed it made most logical sense to call the longest axis the X axis, the axis perpendicular but in plane to that the Y and the axis perpendicular to them both the Z ....
Conventionally, the longest travel axis perpendicular to Z is X and the shortest is Y. This is regardless of stock loading and operator positioning. Schools and online courses teach this. I'm pretty positive ISO and the EIA cover this in their machine design standards for machine axis nomenclature as well. Be known, manufacturers don't have to abide by these standards and neither does the individual hobbyist. Generally, work is done in the 1st quadrant. That is, X+ is to the right and Y+ towards the back. Loading a router with the tool positioned at machine home in the lower left of the long axis is awkward at best because the gantry is in the way. let alone positioning your machine the long way against a wall instead of the long axis parallel with a wall is also unusual. (EDIT: Even gantry mills in the iso standard have the long axis designated as X). For some reason many here reverse X and Y in discussion. It doesn't make a difference what you choose to use at home, but if you post questions on other forums then consider this or you might attract the purist scythe.