Feral cats are the offspring of lost or abandoned pets or other feral cats. They are usually wild and having had no human contact, are fearful of people. Some feral cats, with time and patience, can adapt to being pets.
Stray/Homeless cats are pets that are lost or have been abandoned. They are accustomed to humans and generally will accept handling by people. These cats are often adopted by caring people.
With most pets being microchipped, if you wish to adopt a stray cat, have him/her checked for one. Ask your local shelter, neighbors, your veterinarian if there have been inquiries about the particular cat. There may be a family searching for their lost pet.
Be aware that stray/homeless cats that have been on the streets for any length of time may adopt feral behavior.