"Period" in art, refers to a space of time in which a number of artists, sometimes independently from one another, begin to study a similar style or to paint in a similar style. Examples of this include the Renaissance period and the impressionists. To create a studio project based on a period you should study the period of your preference in depth and learn to create in the same style that artists from that period created. For example, if you are doing a studio project on Italian Renaissance Fresco painters, you will need to learn to mix paint and create plaster murals in their style.
Pointillism, pop art, cubism and fauvism are all examples of styles of art. While many of these styles can be found reinterpreted by contemporary artists, they remain valid topics for studio projects. Unlike a project based on the period, you will probably not need to make your supplies but it is expected that your art be true to the genre you choose to work in. An example of a style based project would be to re-imagining modern life as painted in the impressionistic style.
There are hundreds, if not more, types of art, many of which are no longer practiced. A project based on art type can be of particular interest to those studying anthropology as well as art history. Print making from the Japanese style to that practiced by colonial settlers, bead making, glass firing, mask making and traditional doll painting are examples of different types of art but there are many more to choose from. A possible project could be to create kachina dolls or you could paint them, for a modern take on an ancient art.
Creating a project based around a single artist can be somewhat more difficult than the other ways to approach a project. This is because people already have expectations based on the reputation of the artist and your project may not live up to those expectations. However, if you are making a study of a particularly accomplished artist who worked in a variety of styles and media you will get a chance to explore a wide range of artistic styles and media you would otherwise be restricted from. An example of a project based on an artist might be one about Andy Warhol who created paintings, prints and movies, although he mostly worked in the pop art style.