What exactly do researchers mean by these terms, and are they the same? The CDC defines loneliness as "the feeling of being alone, regardless of the amount of social contact." Social isolation refers to a lack of social relationships. Some people experience loneliness as a result of social isolation, whereas others may feel lonely despite not being socially isolated. Humans are social beings, and as such, we need to interact with others in order to comprehend our role in the world. Our connections with others enable us to survive and thrive throughout our lives.
How can you aid someone who is socially isolated? Invite them to social events or classes you are attending. Find out if local senior centers have activities that are free or at little cost. Go with them. Help them get introduced, and participating.
Either side of the coin is difficult: if you are lonely or alone, it can be frightening to seek out others with whom to connect; if you fear someone close to you is isolated, inviting them along might feel invasive (especially if you don't know them well). But I would advise you to take a chance and reach out; it could make both their and your day!
Here are a couple of articles for more information from the National Institue of Aging and CDC.