The round can be very confusing. Hopefully this page will help straighten it out for you. In the simplest terms, the Round is the whole back leg of the beast. The photo shows a crosscut across the big end of the Round.
Compared to the Chuck (Shoulder) at the front of the beast, the muscles of the Round are much larger, much leaner and easier to work with than the smaller, more complex muscles and bones of the Chuck. They are also tougher, take longer to cook, and with so little marbling fat they are less flavorful.
First Confusion: Top & Bottom: These designations have nothing to do with the cow. When a meat cutter slams the Round primal cut down on the cutting table to start cutting, the Top Round is up and the Bottom Round rests on the table.
In relation to the cow, the Bottom Round is on the Outside, away from the backbone. The Top Round is on the Inside, closer to the backbone. In other words, the photo shows a top view of the right rear leg of a cow that is facing to your left and tail to your right. For clarity, the Top Round is at nearside (bottom) of the photo. That on the forward side (Knuckle) is much shorter and usually handled quite separately.
The Ends: The Top, Bottom and Eye rounds all run from the Sirloin End (the big end) to the Shank End (the small end). These muscles are at their tenderest (not really tender, though) at the Sirloin End, and become progressively tougher with more connective tissue (and more flavor) toward the Shank End.
The Leg Bone: All the "Round" is to the right of the leg bone in the photo. To the lower left of the bone (forward side of cow) is the Knuckle cut (Sirloin Tip). The long "tail" stretching around the edge is not usually included with the Round or the Sirloin Tip,
Top Round: This is the two big muscle at the nearside (bottom) of the photo, and aft of the Leg bone. It is on the side of the leg closest to the backbone and is generally more tender than the Bottom Round.
Bottom Round: This is at the farside (top) of the photo, and is composed of the block shaped muscle and the wedge shaped muscle. This is on the outside of the leg, away from the backbone, and is generally tougher than the Top Round.
Eye of Round: This is the oval shaped muscle at the upper right in the photo. It is on the outside, away from the backbone and at the rear of the beast, but is more tender than the Bottom Round.
Knuckle / Sirloin Tip: This muscle structure is on the forward side of the leg bone, to the lower left in the photo. It is normally handled very separately from the meat aft of the leg bones, and not considered part of the Round except in a full cross cut like the photo cut.
Rump Roast: This cut is from the Sirloin end of the Bottom Round - in other words, it's up at the rump of the beast.
More on Cuts of Beef.