Three Coat Stucco System: Today's stucco is made from Portland cement, lime, sand and water in it's most basic form and is still what a lot of stucco contractors use because of the strength and being a cost effective formula, in addition.
Plastic cement is usually used instead of a common cement and lime because it has a predetermined amount of lime added to it already which makes a perfect consistency for plaster mud after sand and water is added. Plastic cement is basically common Portland cement and lime mixed together in one convenient bag.
The basic recipe for stucco base coat is three parts sand to one part cement (plastic) and approximately 3 to 5 gallons of water, depending on the consistency you're going for. I made a post that goes into much greater detail on how to mix stucco base coat and is worth checking out if you are looking for more information on the topic.
One Coat Stucco System: One coat stucco is a little bit different than a three coat stucco system and uses a much thinner base coat (3/8") so the cement used is a little bit different than a "standard stucco mix".
The base coat for a one coat stucco system consists of Portland cement, chopped fiberglass, acrylic additives, sand and water and is modified like this because it is much thinner so the fiberglass particles and acrylic additives give it a little bit of strength and makes it a little bit more water resistant than traditional stucco base coats. Here is a product page for Omega Stucco's (One Coat) base coat that will give you a little more info on what's in it.
Finish Coats: The finish coat is the final coat that goes on a stucco wall and is usually colored (integral coloring added to product) and can be a standard cement based finish or an acrylic type of finish.
A standard cement-based finish will use white Portland cement, sand and water that is mixed with a color packet (powdered) which tints the finish product to achieve the desired color that you want. Typically you would choose from a stucco color chart to achieve the desired color your going for but you can also order a custom stucco color, if you would like.
An acrylic type of finish is a lot like paint but has aggregate included into the mix that gives it that "textured look" and is comprised of acrylic, crushed aggregate (like crushed quartz) and color pigment.
The base for acrylic stucco is usually white and a color bottle (liquid) is mixed to the base to achieve the desired color, which is also chosen from a stucco color chart. Acrylic stucco finishes have much more vibrance to them and are brighter in nature and you can custom color match just about any type of color, even specific paint manufacturers colors.