Two different things wearing one word

Alone is a count. How many people you saw this week, how many messages you answered, whether anyone was in the house when you got in.

Lonely is a gap. It is the distance between the connection you want and the connection you feel you have. It is not a number and nobody else can see it.

The two do not track each other nearly as closely as people assume. Some people live by themselves, see two friends a month, and are content. Other people are in a full house every evening, at the masjid three times a week, and are as lonely as it is possible to be.