A circle refers to a select group of people who interact socially. If someone refers to his or her circle, they mean the people they choose to be friends with or associate with because of similar interests or concerns.
Ex: I hope Lance and Laura will enjoy the cocktail party. I know that the people we have invited tonight are not in their usual circle.
Ex: I have never felt the importance of having a circle of friends more than last week when I had emergency surgery. Having people there for support is one of the things that I believe helped me to recuperate faster.
A circle can also refer to a group of people sitting or standing in the shape of a sphere. A group of people can be asked to form a circle, or can form a circle on their own initiative. You might see a group of sitting in a circle as well.
Ex: A circle had formed in the midst of the plaza as people gathered to hear the young girl playing the violin.
If you refer to a crowd, you mean a large group of people that have assembled in one place; a throng of people.
Ex: One of my scariest memories is being separated from my parents in a large crowd during a busy Christmas shopping day.
Ex: Though he tried to make himself heard above the crowd, the elderly man's voice was drowned out by the din.
If you crowd someone, you are moving in on their space, or moving to close to them. In this expression, crowd is used as a verb.
Ex: Please don't crowd me! I am moving into the elevator as fast as I can with all of this luggage weighing me down.
Ex: When the young man fell to the ground out of breath after the race, the nurse warned others not to crowd him, but to give him some space.