Key difference: Ceramics is a general term that includes pottery. Pottery is entry-level work. Ceramics is higher-end professional-grade work.
Ceramics and pottery are used interchangeably ay times, which is not a problem as there is little difference among the words. The words both refer to an art form which shapes and molds clay. However, technically speaking, the word ceramics is a more general term and it includes the term pottery.
Pottery refers to using clay to make useful things. Ceramics includes pottery, but also ceramic inlay for teeth, ceramic knifes, ceramic tiles, etc. In reference to art, pottery is generally thought of in terms of less sophisticated, maybe entry-level work usually creating useful items like plates, mugs, vases, etc. Ceramics, on the other hand, it used to refer higher-end professional-grade work, especially sculptural items which mainly have a decorative value like as a clay sculpture, decorative plates, etc.
Ceramics are frequently thought of as pieces of fine art that are created to be visually appealing rather than have a function, whereas, pottery is used to describe something that is useful, that serves a purpose in daily life. Other than the method of used, there isn’t much difference between ceramics and pottery. Both are made the same way through a process of forming, firing, glazing, and re-firing.
Each piece is made by forming a clay body into objects of a required shape and heating them in a kiln to high temperatures which removes all water from the clay, this induces reactions that lead to permanent changes in the clay including increasing the strength and hardening and setting the shape. The body can be decorated before or after firing.
There are three main types of ceramics and pottery: earthenware, stoneware, and porcelain.
Earthenware is the earliest type of pottery, which is made from clay by firing it at low temperatures in pit-fires or in open bonfires. This type is usually handmade, undecorated, and has a porous biscuit form that is has limited utility for storage of liquids. Stoneware is a bit more advanced and needs a kiln that could be fire it at higher temperatures. Stoneware is usually glazed. Porcelain was first made in china and is famous for its delicate and slightly transparent appearance. It is made by using a special form of clay called kaolin.
So, to put it briefly, pottery is simpler and older. It was born out to need for storage and usability. Ceramics, on the other hand, leans more towards art and decoration.