drill is the finished size of the actual hole. diameter is the outer diameter of the copper surrounding the hole. The annular ring of the via will be the (diameter-drill)/2.
Default settings refers to values of current technology in PCB manufacturing industry for drilling or corrode the copper. Don´t means that necessarily must exists relation between both minimum values.
Eagle gives you a drop down menu of many different sizes, but you're not restricted to those sizes, you can type in any number you want. 0.5mm drill hits are pretty big, most fabhouses can do 0.25mm no problem.
A via will be drilled my the manufacturer with a drill size 0.1mm larger than the finished via hole size. It is the FINISHED via hole size that you define in your EDA package. Refer to IPC-2221 and IPC-2222 for full details on this and other factors such as tolerance stack ups.