People who are alone might be lonely, but not all of them are.
People who are lonely definitely need company, although that should also be company of choice, people who make them feel good, who can sympathise with them. It is also easy to feel lonely even when surrounded by people, particularly individuals that you do not like.
For people like myself though (this may be the impact of getting old), I enjoy my time on my own, particularly if there is work to do and I do not want to be distracted. Much as I love my wife's company, it is often far harder to concentrate when she is home all day!