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My understanding is that terracotta is clay made into a figure then baked, such as the Terracotta Warriors of China. But earthenware and pottery both refer to baked clay, so how are these different? And does the following mean the same?

Terracotta pot

Earthenware pot

To make clay into pottery it is fired. Different clays contain a different mix of minerals. When it is heated to about 1000 °C, some of these minerals partially melt, and cause the clay to turn into a ceramic.

There is a limit to how hot you can heat the clay. If you make it too hot, the clay will melt, and sag in the kiln. In extreme cases the clay can melt completely and the pot will become a puddle (You then have a big job scraping melt off the kiln floor.)

Some clays can survive higher temperatures. These can be heated to 1200 °C or even higher without sagging. At these temperatures the clay particles bond together to become waterproof. This is called "stoneware". A particular type is "Porcelain" that has a large amount of kaolin clay. Porcelain is especially strong, so it can be made very thin.

Most clay can't be heated this much, and is heated to 950-1150 °C. At these temperatures the clay particles are bound less tightly together and the fired body can absorb water. This is called "Earthenware". Earthenware may be white, grey or red and it is often glazed to make it waterproof.

Terracotta is one type of earthenware. It is an iron rich earthenware (and so a rusty red colour) that is often left unglazed so that it can absorb water. It is used for a range of applications. Plant pots, flooring and roofing tiles and storage jars, but not usually for plates, cups or other crockery.

So Earthenware refers to the type of clay, and terracotta is a type of earthenware.

Earthenware is a general term for a material made by baking clay, sometimes together with other minerals, and for items made from that type of material, e.g. tableware. Terracotta is, in general usage, a particular type of earthenware. The relationship (or "difference") between them is like those between "vehicle" and "bus", or "metal" and "iron", or "nation" and "Japan".

Terracotta is not just used for making figures; many useful articles are made from it, including plant pots, tiles and water pipes. The word also has a number of specialised meanings in art, archaeology, etc.

Earthenware (Oxford Dictionaries)
Earthenware (Wikipedia)
Terracotta (Oxford Dictionaries)
Terracotta (Wikipedia)

The definitions are taken from the Collins Dictionary:

Terra-cotta is a hard, brown-red, usually unglazed earthenware used for pottery, sculpture, etc.

Earthenware bowls, pots, or other objects are made of clay that is
baked so that it becomes hard.

Terra-cotta pots:

Earthenware pots (just a couple of examples):

So, terra-cotta stuff is usually unglazed. Also, terra-cotta refers to the color (see the picture of the pots above). Earthenware doesn't refer to that color, earthenware can be any color, basically.