Lonely vs Alone

Lonely is when you have someone, but they are not there at that time. You have have something and you mean something to someone. Alone is when you have no one. You mean nothing.

From personal experiences, I have felt both alone and lonely at many points in my life. When I was sitting at lunch with no one, I was both. Alone because no one was with me and singled out. Lonely because my friends abandoned me, they left me.

Technically, alone is a synonym of lonely.