As with all other rocks, there are three beach stones types according to how they originated: Igneous, Metamorphic and Sedimentary beach rocks. The first two types of rocks, Igneous and Metamorphic, are formed after molten rock from magma and lava eventually cools down and finally hardens into rock again. To these beach stone types belong pebbles like: quarzite, granite, slate, pumice, marble etc.
Sedimentary beach stones are formed on shores or in the water by the weathering of older stones. These bits and chips of older stones settle to the ground on layers along with the remains of organic materials, like parts from plants and animals. Through time they harden into compact sediment. Fossil stones found on the beach are this kind of rocks. Other examples of sedimentary rocks and beach pebbles are: sandstone, shale, conglomerates and breccia.
Depending on the geological history of the place, beach pebbles and stones could be a variety of the above kinds of rocks (igneous, metamorphic, sedimentary) with a change in percentage of occurance of each rock kind.
Also, rocks and beach pebbles too, are composed of minerals. So one could group stones according to what mineral they are made of. Jasper and agate stones belong to the quartz family. But not all stones are composed of only one or two minerals. In that case, a rock or pebble stone will belong to more than one mineral groups.
Minerals are composed of chemicals. For example, a quartz pebble and a jadeite pebble belong to the chemical group of Silicates. A malachite or dolomite pebble are members of the Carbonates, Nitrates, Borates group. So this is another kind of possible categorization. According to petrologists, who are scientists that study our earth's geological history and geological formations of stones, mineral groups are subdivisions of the three general types of rocks I mentioned in the beginning.
For a more detailed explanation and a deeper analysis of the different types of stones and pebbles go to the following resources:
Igneous Stones and pebbles from Wikipedia
Metamorphic Stones and Pebbles from Wikipedia
Sedimentary Rocks and Pebbles from Wikipedia
Information on Minerals and Rocks from Mindat.org
It is important for all who have an interest in beach rocks and pebbles to have basic knowledge on beach stones types. However, depending on what you have in mind to do with your beach rocks and pebbles (for example: use them for decoration, make crafts, use them for art inspiration) and how you would like to express your creativity (beadwork, photography, drawing, writing, making wall art etc.), except these scientific ways of categorizing them there are other more "artistic" ways to group stones and pebbles. You could choose to sort them out by shape, color, size or texture, which proves practical for your art and crafts projects.
Go from Beach Stones Types to Beach Rocks Info
How to identify Pebbles and Beach Rocks
Learn about Beach Gemstones