I see that the dictionary spells them both ways(Travelled and traveled-Traveller and traveler), and I can't find any information on the difference.
You just showed me the definition of "traveller" (two L's), which says chiefly Britain. You might see "traveler" in the pronunciation guide, but that's not the spelling. If you click on the link for "traveler," it brings you to the page I linked to. Here is traveller: The only spellings in that definition that have one L are the pronunciation and the link to the U.S. spelling. Here is some information at the bottom of "traveler": Take also this link. I'd hate to turn this into a back-and-forth, but, simply put, with two L's, it's British, even according to the link you sent. One L is the U.S. spelling.
In British English we ALWAYS spell it with a double 'l': 'travelled/traveller/travelling etc'. Every American English textbook I have used spells it with only one. There is no other difference.