Ok, here is a basic diagram showing the difference between diameter and circumference.
Basically, if you measure in a circle around the rod handle, that is a circumference. The diameter is a straight line measurement from one side of the handle to the other, its basically the thickness of the handle.
Do your best to measure the thickness of the rod handle at its thinnest spot and its thickest spot. I will throw some numbers out there for an example.
My handle on my calico surf rod has a diameter of 25mm at its thickest and 24 at its thinnest. I would need to buy the 30mm, 35mm, or 40mm tubing. This tubing will be larger than my rod handle so can be slid onto the handle but will shrink down to an Inside Diameter of 14mm, 17mm and 19mm which is smaller than my rod handle and will ensure a tight fit around the handle.
When thinking of inside diameter vs outside diameter, think of a washer you would put on a screw or a bolt. The diameter of the center hole is the Inside diameter. The diameter of the entire washer is the Outside Diameter. The distance between the outer edge and the edge of the hole is its thickness or "Wall" measurement.
Now for some math. If you are having difficulty measuring the diameter, then measure around the rod handle, this is the circumference. In my example above, I got around 80mm.
Your diameter equals the circumference divided by 3.14. Thus "Diameter" = 80mm divided by 3.14, or 25.5mm.
Since in my example I have 3 different sizes I can choose from. I can make a choice based on how thick of a rubber coating I want over the cork. The more the tubing can shrink towards its smallest size, the thicker it will get.
Thus the 30mm tubing will shrink the least as it it the closest in size to my actual handle and will be thinner than the 40mm tubing which will shrink the most and will end up thicker. The 35mm will be right in the middle of the other 2.
Thickness may be a consideration based on durability standpoint. Thicker will mean a slight increase in durability, but will also add a very slight amount more of weight to the rod handle.
I hope I explained this well enough Eric. I'm sure Skrilla will chime in something is incorrect.