Oil Stone vs Water Stone
These two conventional terms suggest that certain stones are best used with oil as a lubricating medium while others perform better with water. However, this is not the case as all sharpening stones can be used with either lubricant - or none. Of course, the use of water or oil can be beneficial, and lubrication helps to prolong the life of very fine, expensive varieties like Japanese water stones.
Natural Sharpening Stones vs Synthetic
Natural vs synthetic whetstones is perhaps the biggest binary when it comes to blade sharpening.
The natural sharpening properties of hard minerals like quartz have been known and appreciated for many years, but nowadays, the available options have been considerably expanded by the addition of artificial bonded abrasives like carborundum (silicon carbide) or corundum (aluminium oxide). These can cut more quickly than the natural alternatives but do not typically include very fine grits.
India Stone vs Arkansas Stone
India Stone is a widely used medium honing stone made from aluminium oxide. The term is actually a brand name owned by the Norton Adhesive Company. These whetstones have a distinctive orange and tan colouring.
Arkansas stone, by contrast, is a natural sharpening stone made from a variety of quartz, as explained above.
Ceramic Sharpening Stones vs Water Stones
As the name suggests, ceramic sharpening stones are an artificial variety made from a fused block of ceramic material like silicon carbide (ceramics are hard materials made via heating, which contain no metallic or organic material). Ceramic sharpening stones are very hard-wearing and are normally used dry with no lubrication. They are typically available with medium and fine grit sizes.
By contrast, water stones can be both artificial and natural in origin. As discussed above, water can be used for lubrication when sharpening with these stones and it will make the process easier, but it is not essential in most cases.