The short answer is that there is no difference: they mean pretty much exactly the same thing, they just sound a little different. 'Recently' always referring to something that happened more than a month ago is just wrong. The main difference is that 'lately' is more likely to be used to refer to an ongoing situation whereas 'recently' is more likely to refer to a single event, but they're pretty interchangeable. 'I've been cleaning out the chicken coop lately.' 'He died recently.'

They are used as the same word. You can choose which one you want to use.