The numbers are the rating; RON and AKI are units. Different places use different units. The small print next to the number will tell you which unit your station serves. Different stations may have slightly different numbers—just choose the one that is as close as you can to what is recommended in your vehicle's manual.

Unleaded is because old fuels used to have lead in them but leaded fuels are bad for modern engines and, turns out, breathing an atmosphere with lead in it is not great.

Diesel is just a different fuel entirely and has entirely different properties. Diesel and gasoline are not interchangable.

E-10 is gasoline and ethanol mixed at 10% ethanol/90% gasoline. Some places may have E-20 or E-85. Here in the States it's standard to have a low percentage of ethanol mixed in. Small percentages can still be ran by a normal engine whereas the engine will need to be tuned to run higher percentages such as E-85. "Flex Fuel" cars can run pretty much any mix percentage because they have ethanol content sensors and will adjust the tune as necessary.

Fun facts:
Ethanol is a type of alcohol and is a biofuel commonly made from corn.
Ethanol is popular in the performance tuning world because it has a higher energy content but it requires significantly more fuel to be burned.

Some planes still run on leaded fuels.