Only one character can be played at a given time (in similar fashion to how the player may only access one world at a time), but the player is free to create as many characters as they desire.
The term player is often used as a synonym with character, but may also refer to the person accessing the game if the topic is unrelated to character mechanics. All of Terraria's gameplay revolves around actions performed by the character, and the camera is nearly always locked to place the character in the middle of the screen.
The term character or avatar refers to the figure controlled by the player through the game controls.