Quote from TransmorpherDDS >>

I won't say that this is the "difference" between the two, but I think a big indicator of an RP-heavy playstyle vs. an RP-light playstyle is how much the players actually care about NPCs.

RP-Heavy players will treat NPCs as real people... they'll care about trying to avoid traumatizing young people in a crowd, they'll chat casually with the shop keepers. An RP-light playstyle will treat them more as a function within the world... sure, they'll actively interact with the important characters that are clearly part of the story, but otherwise they're aware that the NPCs largely don't matter, and unless the DM is really pushing them for harder RP, dismissing or insulting NPCs when you're done with their function isn't going to have any kind of serious repercussions for the characters. If anything it might lead to some funny moments at the table as the players clown on some random NPC as a gag before marching off to do gameplay stuff.

Quote from Linklite >>

I see a divergence in how people are defining roleplay in the thread. Some consider it to be referencing the level of engagement with their character - are the players making decisions based on their interpretation of their character? Do they engage with the world? Are they interested in the worldbuilding? Are they playing the role of their character? Or are they playing a hack 'n' slash that is about stuffing the game with as much fighting as possible? The other interpretation seems to be the level of engagement in the storytelling aspect of the game. Do they describe the spells being performed? Do they describe everything as though it's a novel? Or are they skimping on the details and focussing on the general facts?

I can see both as being valid, but they are describing two different qualities and although they can be correlated, they should be distinguished between.

Quote from theologyofbagels >>

Quote from pavilionaire >>

You might be a heavy RP group if you have to check with your fellow players to make sure it's just your characters that don't like each other, not the players.

 Underrated comment. Five stars.

Personally, I find the difference between light and heavy RP to be the degree to which players inhabit their characters. If your group is happy spending an entire session chatting in character, wants to learn each other's secrets, gets emotionally invested in the lives and quandaries of the PCs, have frequent fireside chats in the aftermath of combat or narrative beats, and has to temperature-check after conflicts arise in-character...yeah. I think that's an RP-heavy group. 

 
Thank you for your answers, as these are the responses I was really looking for as, indeed, players seem to draw different meanings from the term "Heavy RP." I’ve struggled over the last few years to filter through players who are drawn to the “Heavy RP” title in my LFP threads, but find that they aren’t actually what I’m wanting in my games.

Emotional investment in the world and PCs and NPCs, engaging with the world and characters, wanting to learn the ins and outs of the other players’ PCs (their secrets, fears, just as mentioned), just chatting in character for a whole session whilst making no actual game progress at all, making decisions and playing the role of their character, etc., this is the meaning I always took from the term “Heavy RP” and is really what I’m searching for in potential players.

Your answers will help me communicate in the future what I’m really hunting for. However, is there perhaps a better word to use than “Heavy RP”?