The printer I am using is an Artillery Sidewinder X1. In the photos attached you can see that I am having a lot of inconsistency between layers. The problem has never gone away and I always thought it was Z wobble but now I'm not so sure it is because we have tightened everything up, making sure everything is stable and tight. Is this Z wobble or is it something else. Could it be the filament? Does it have anything to do with the slicer settings?
No, this is not Z-wobble, Z-wobble is usually characterized by a repetitive distortion, from the supplied images this repetitive pattern is not observed. A Z-wobble pattern is typically caused by the lead screws, or the Z drive where carriage follows the X/Y motion of the lead screw nut.
A typical image of Z-wobble on a Benchy would look like:
Your print doesn't look that bad for a low-end 3D printer.