its really olny the british that call them flatbows. Europe and US, all call them longbows.The flatbow is what is known in North America as a longbow. Where I come from, the UK, the term longbow really describes the ELB, English longbow.
There are some longbow experts on here who will pick this up but mainly it is the profile of the bow, having a riser and an arrow shelf that is different for a flatbow. Google 21st century bows or Fox bows to look at their flatbows then maybe Bickerstaff to look at the ELB, that will show you.