You can buy them from most jewelry suppliers but they are not hard to make for yourself either. They also work great for making chains and using as part of a clasp.
The round jumprings are the most common, and most people find them the most versatile.
However they come in a variety range of finishes (plating), even colours! And tho less common, they can come in many different shapes. They can be manufactured with different types of metals and in different gauges (thickness of the wire).
The stated size of a jump ring is by convention, the diameter of the entire jump ring, measured from its outer edges.
The stated thickness is the size/gauge of the wire used to create the jumpring.
Tho jumprings are most often used to connect clasp to the main jewelry piece or different component pieces together, or to add a dangle to the creation, there is actually innovative, inventive, and other creative ways of using them ~ don't be limited by just using them as connectors!
Split Rings resemble little key rings. Lke jump rings, they are used to connect link/rings or to hang things off chains, necklaces, bracelets, etc. With their double-loops, they are more secure than plain, unsoldered jumprings.
The stated sizing & thickness of a split ring follows the same convention as jump rings.
Where you would definitely choose a split ring over a jumpring, is when you need the linking-connector (ie the ring) to be very secure. For example, when you hang precious charms off an anklet, bracelet, or any other chain jewellery.
Also, split rings are preferable as ending-rings, i.e. at the end of a necklace or bracelet. The ending-ring is often used as the loop to which the clasp (like lobster clasp, or hook clasp) will latch onto to close off a piece of jewellery.
The reason why this is so is because split rings are much more secure than jump rings because the split rings have multi-loops per ring and so are many times stronger & less likely to be accidentally pulled open.
You will want to make sure that you do not spread the loops in the splitring too far apart as that will deform it somewhate. You may also find it is difficult when working with a lot of split rings, coz to open them, you may indeed split your fingernails! This is where the incredible Splitring Pliers come in. It will easily open a split ring so that you can insert your charm onto the split ring, or when you want to attach the split ring onto a chain, etc. The pliers are designed to open the split ring easily and efficiently.