@turquoise-- These terms are often used interchangeably.
Not all animals have a circulatory system that functions like ours. Blood, heart and vessels are the major components of the circulatory system in all animals but some have a closed circulatory system while others have an open one.
What we have is a closed circulatory system where blood is pumped by the heart and distributed throughout the body via vessels. Some animals have an open circulatory system where blood and other fluids are not distributed by vessels but rather pumped directly into the cavity where organs are..
All mammals have a circulatory system exactly like ours, composed of heart and vessels.