Both film photos and digital photos can be printer on special photo paper. Printing on photo paper is a process that involves a few stages and is for example very different than printing documents on your printer.
Film photos can be printed on photo paper in two stages. The first stage involves developing the film itself into what is known as a negative. The negative is then printed on a special photo printing paper in a process that involves a few chemicals and a few stages. Digital photos on the other hand can be directly printed on photo paper as there is no film to develop and there is no need to create negatives.
Printing photo prints on special photo paper involves five stages:
Developer. In this stage the photo paper goes through a bath of a chemical that is sensitive to light. Once the photo paper is soaked with this agent and a consistent layer is present on the paper the paper can be exposed to the photo. This is done by using a very high intensity light projector that projects either the negative or directly the digital photo on the paper. The developer chemicals captures the projected photo.
Stop bath. In this stage the photo paper goes through a bath of a special chemical that stops the developer chemicals reaction. In other words the stop bath is a chemical that negates the developer chemical characteristics. This is done by the stop bath chemical washing away the developer chemical. Once soaked on the stop bath the developer agent on the photo paper loses its light sensitivity and no longer changes when exposed to light.
Fixer. In this stage the photo paper goes through a bath of a special chemical that fixes the captured photo. Although the stop bath stopped the developer chemical from reacting to light the photo is still not stable and not fixed in place. The fixer chemical bath basically washes any residue of unexposed or undeveloped material making the photo paper completely insensitive to light.
Washed. In this stage the photo paper is thoroughly washed removing any previous chemicals from it. This stage is very important since any residue of non developer material or other chemical can result in imperfections in the final prints.
Dried. This is the last stage. After the photo paper print is washed it is still moist from the chemicals it went through and from the washing agent. The last stage does not involve soaking in any chemical. It is simply implemented by placing the fresh photo prints in an over to dry out. Once dried the photo prints are ready to be used.
The different chemicals used are usually reused over and over again. The longer a chemical is used the less effective it is and the more time it needs to complete its job. For that reason for example a fresh developer agent needs to be exposed to light for a shorter time than an older reused agent. At some point the chemicals efficiency is too low to be used anymore and they are safely discarded.
Danette Mckay explains about this subject in more depth at printing pictures