Plants, fungi and bacteria can be decomposers, and may gain energy from dead and decaying matter, but do not "eat" it as such, so they are not called detritivores. Instead detritivores tend to be animals, such as woodlice and sea cucumbers.
Saprobionts, again, are a type of decomposer, but not all decomposers are saprobionts. Though saprobionts also feed on dead and decaying matter, they are unable to ingest and digest it internally. Instead, they carry out extracellular digestion. Many fungi are able to do this. They excrete digestive enzymes onto the matter and, once it is digested, are able to absorb the basic energy and/or nutrients that they need from it.
Saphrophytes are sometimes defined as any organism that lives on dead or decaying matter, although it more commonly seems to refer to plants, fungi and micro-organisms. For the most part, though, the word seems to be interchangeable with decomposers.
So to sum up, detritivores and saprobionts are subtypes of decomposer (also known as saphrophytes.)
All of them get energy and/or nutrients from dead or decaying matter.
Detritivores ingest and digest this matter within themselves, whereas saprobionts excrete enzymes to digest the matter externally to themselves.