There are some subtle and other not so subtle differences between the cuts, and its not just about your body size, that’s what the individual measurements are for.
Slim Fit: Have shirts cut in a slim fit for a more athletic type of fit. You will find these to be almost form fitting to your body, with higher arm holes and narrower sleeves. The cut to the body will be much more slim, and you will see more “you” in your shirt.
Tailored Fit: Want something that shows your body composition without showing all of your body composition? You’re likely looking for a fitted trim shirt selection here. These are not as form fitting as the slim fit shirts, but are still shaped more for your body. Not loose, but not tight either, these are a more comfortable option with less restrictive arm holes. If you need to look your best daily, but your job has you moving around a lot, this might be a better option.
Regular Fit: First, do not take the description of the regular fit to mean sloppy or unprofessional in any regard. The regular fit shirts are a little more comfortable, but not necessarily more casual, unless you wear them more casually (which could be the case regardless of the cut). These still have a nice fit to the body, as should all custom clothing items, but have fuller sleeves and wider arm holes for maximum range and mobility. These shirts are certainly for a more relaxed, but still professional setting.