My understanding is when you get a low cost print from a drugstore or by mail you are ordering what is called a C-print, which is similar to the old enlarger method in the sense that there is paper with light sensitive coatings that gets processed in a series if chemical baths. Except instead of an enlarger projecting the whole image the paper is exposed with LED lights or lasers. The quality depends on the quality of the coated paper which can range from very high to not so high, also the quality control in refreshing the chemistry, and and the resolution of the lights. So good results are possible.
Another method is inkjet/giclee which does not use light sensitive paper. This is what home printers use, and there is a huge range of quality in the paper that is chosen and the resolution and quality of the printer. but can be taken to a very high level in commercial printing with specialised RIP software and large format printers. With what they label fine art prints pigments rather than less lightfast dyes are sprayed from nozzles onto paper, and the choice of fine art printing papers is broad in terms of texture, thickness, base color, etc. You can get a free set of samples from places like bay photo or paper makers like Hahnemuhle. These can be extremely archival and top quality.
The way I get how acrylic prints are made, a paper print is fused permanently to the back of the acrylic and sometimes a sheet of aluminum protects the back. For canvas prints you can choose to have a paper print fused under pressure to the canvas or have the inkjets spray directly on the canvas. Metal prints I understand are made with inks infused into the base metal either white or natural metal and a protective coating is sprayed over that matte or glossy, etc.
To me it is part of the art to choose the print treatment. Some images call me to go for fine art paper of a certain texture, others evoke canvas or acrylic or metal. It's all good because it's the form of the work the artist chooses, just as a painter might choose to work on canvas or paper or a panel or plywood or directly on a wall or ceiling.