What's the difference between a 10 amp and 13 amp extension lead?

what a mess of ignorance,, especially the "size of the flex" nonsense...the diff is... the smaller the gage number--- the larger the wire inside = the higher the load you can use on it.
so a 10 gage wire will carry more than a14 gage,,, this is usually how extensions are rated not by amps.... however if it says amps then the higher the number is best. just remember,,, most outlets only have 15 amp breakers !!!!!!! using an extension of 30 amp size will not let you put more than 15 amps on the breaker also you need to decide how much you're active to load the extension with to establish how long the cable needs to be,,,,,,,,,use the shortest extension near the gage wire you need...long extensions have more resistance and either the cable can burn or cause damage to your equip!!!!!!!!!!!!!!!!!!!!!!!!!!