The narrator of "Rebecca" was a companion to a wealthy American widow. They were holidaying in Europe when the narrator met Max De Winter and quickly became his wife. This person was a well-brought-up young woman who had been left orphaned with little or no money. She did errands for her employer and accompanied her on outings if required. I think the novel is set in 1920s or 1930s. There's at least one character in a Dickens' novel who was a companion. Some companions may have been poor relations of their employer's family.
A companion's duties might vary depending on requirements of her employer.
As to the other meaning of the word - Camilla Parker-Bowles used to be described as the companion of the Prince of Wales.
If the woman's occupation was companion in 1940s it was more likely to be the first meaning. As others have said, she may have been a mixture of carer, maid, housekeeper & cook to an elderly woman or invalid, or just someone to be present and do errands.
