I am sure most of the gamers reading this post have seen these similar terms and noticed the subtle difference in the spelling - just one small letter changed from an "e" to a "l" in the middle of the word. Of course, there must be a difference in the spelling of these two words since they do, in fact, have different meanings. I believe a quick example of each term will better illustrate the difference between them instead of repeating a textbook definition. For the following example, I will assume that there is one Dungeon Master and two players; one a role-player and the other a roll-player.
The characters have been exploring each room in an abandoned mine complex. As they are leaving one room to enter a hallway, the party of adventurers run into a group of Orcs scavenging remains in the caves.
Dungeon Master: The Orcs drop the valuables they had just picked off the remains on the floor and put their hands on their swords. The leader snarls and declares, "What are YOU doing in here?".
Role-Player Ralph: I hold up my hands in a non-threatening manner and say, "Surely, there is enough valuables laying around for all of us to get some?".
Roll-Player Ron: I negotiate with the Orcs. [rolls d20]
That simple example should serve to illustrate the difference between the two play styles. I am just pointing out the difference between the styles and not the merit of each. In my opinion, it does not matter how you are playing as long as you are having fun. This is not math - where 2+2=4 is always right - but a recreational activity.
I have played using both styles and switch back and forth depending on what else is going on. If we are just cruising through the game while chatting away about movies and stuff then I slide into roll-player mode and just make a quick statement and roll the dice. If we are doing some focused gaming then I will go in depth with the descriptions. I have fun either way.
I feel the same way as a DM. If you want to interact by role-playing in great detail how your character is attempting to negotiate, pick a lock, etc. then I am all for it and will encourage that by occasionally giving a bonus to the roll or I might ignore a failure at times. If you want to interact by making simple statements such as "I attack" or "I negotiate with..." or something similar then I will in all likelihood proceed according to the results of the dice when it comes to success or failure. Who knows?