Reproductions reproduce an image that has already - or originally - been produced in some art medium. The original can come from any source but is most commonly an acrylic painting, oil or watercolor. In earlier years, other techniques were used. But today, a photograph of the original is taken with a high-resolution camera, and then scanned. The scanned image is then used to create a reproduction, or a copy, of the original painting.
This can be done in a variety of ways. Today, the most common means of printing is digital, because the repros can be “printed-on-demand”, as needed, and they can be printed on virtually any surface, or substrate (in art terms) - paper, canvas, t-shirts, china - whatever. Canvas wall art and all kinds of papers are the most frequent for art purposes, but the other uses are quite common.
Although there is technically no limit whatsoever to the number of copies that can be made from the scan, sometimes people do these in “limited editions” and sign and number them. If it’s an artist and they are trustworthy, this information may well be reliable. If it’s a corporation, watch out. However, since there is no actual artist participation in the production, it’s highly unlikely that there will ever be any real value in the product other than decorative, regardless.
Art Prints is a misnomer. There is really no such thing. This is just a term that some people have recently put into use. Actually, “art prints” is so general as to be meaningless. It might as well be the same thing as “prints”, and can easily apply to anything that is printed, including reproductions as above. If you wish to be correct, the term Original art is the most correct to distinguish reproductions from prints that artists actually make themselves or have active participation in. Now let’s talk about those.
There are many kinds of printmaking, and when we use the term “printmaking” we are referring to hand-printmaking, and not giant machines turning out zillions of copies, which is merely printing. The link to an artsy page that Sandy included in her answer, 9 Types of Printmaking You Need To Know describes many of them.
Some artists, both in the past and present, used printmaking as their primary medium. William Blake was a master printmaker, as were Durer and Rembrandt. In some of the current printmaking techniques, the artist does the work from start to finish, in others, he/she has a more supervisory role or something in between. But in all, the artist is part of the process, start to finish.
Handmade abstract wall art is each different because the inks will never be exactly the same on the paper each time; and in some techniques, the plate has to be wiped and shaded by hand with the printing of each impression, further ensuring uniqueness. This is why although they are multiple impressions of the same image, they are indeed each original. Some printmakers do, even more, hand-painted or embellishing works so that they become as painted as they are printed. Sometimes, original multiple plates are created only for printing. In these cases, they do not refer to or copy an image in another medium at all and the editions stand completely on their own.
Original multiples are always editioned and of limited number and signed in pencil. The numbering system was developed centuries ago before copyright laws existed. There are two numbers on a print: a top number, then a slanted line, then a bottom number. The top number designates the number the particular print is within the edition. The bottom number represents the total size of the edition.
Printing techniques have improved over the years, so these are often less important than they used to be, though of course, the total edition size matters. The placement in the edition used to matter because early printmaking was generally etching or similar, done on soft ground metals, which degraded as the edition progressed. Therefore, the early numbers were sharper and more valued. Signing in pencil was customary because pencil lead resides in the fibers of the paper, and cannot be bleached out like an ink signature might be.
Sellers of original multiples should also always disclose the size of any other editions published on other papers or inks or any other conditions. Also, the status of the printing plate should be disclosed - whether it is still extant, or if it has been defaced or destroyed. This is important because otherwise there are no guarantees about continued printings. Many Rembrandt prints being purchased today are reprints from old plates that have been “reclad” in steel. They are not original Rembrandts at all, but an innocent purchaser doesn’t know that and it is rarely disclosed by the high-pressure galleries that sell them.