The distinction is probably easy to miss. If one is playing a game in support of one's learning, perhaps you could be said to be gamifying your learning (if that's even a word). "Gamification", though, refers to using game-like elements in the classroom, not necessarily inside a game environment. "Game-based learning" refers to using a game in support of your learning.
This article by Jordan Shapiro is the most well-explained thing on this topic i've seen.He talks about how gamification systems are seen in places like coffee shops, with their loyalty programs. Gamification, I think, broadly, could be said to be about modifying human behaviour to better reach a goal (free coffee, perhaps, or better learning outcomes in Math class).
I loved his examples of video games we learn from. I agree: students learn from every game they play, whether it's the new "2048" app craze (powers of 2), Angry Birds (physics/geometry), or Call of Duty (single-minded concentration and pursuit of goals, teamwork, reading and writing skills when playing online with others, communication).
It's interesting how viewpoints have changed on the video game issue. I remember even 6-7 years back debating their merits with students. It would seem they have been allowed into mainstream culture (and educational culture) in a way that wouldn't have seemed possible even a few years ago.
Here is where I write a letter to my 13 year old self:
20+ years from now, you won't have to hide your comic books, and video games will be everywhere. Have faith and be patient. Let's hope Zack Snyder doesn't ruin Bruce Wayne like he ruined Kal El! PS: you have two children and you don't have time to play games, but all libraries have lots and lots of comics for you to check out.
Older, more bearded you.
Therein lies my problem with gamification. If we are truly focused on big ideas and learning goals, side quests (for example to get "badges") might get in our way. I also believe in naturalizing the classroom environment as much as possible- so for me, gamification systems would only get in the way of conversations and interactions. Lastly, and my main concern perhaps, is that focusing on gamification systems might undermine students' intrinsic motivation. Put it to you this way: if I don't need a coffee, or even want one, and I notice I need one more sticker on my McDonald's card to get a free one, will I go? Further, a quick search on this subject reveals many corporations are looking at gamification strategies to modify their consumers' behaviour, which doesn't bode well for it's future in education.
Game-based learning suits me a lot more. Minecraft, for example, has been absolutely amazing as a tool in Math class. But what's worth noting there is the differentiation: students CHOOSE to become immersed in a game environment, and only IF they can meet their learning goals with regard to the mathematical concept or big idea under consideration. The other big thing here is that there are NO goals when one opens a world in Minecraft. There are no badges, achievements, or levels. Perhaps Minecraft is the least gamified of all games; even earlier sandboxes like Grand Theft Auto had missions that you could choose to complete (and most players probably did).
Game-based learning is no simple panacea. Differentiation is key. Many games are too closed ended to be useful in the classroom beyond one single set purpose (and there is nothing wrong with that, in those instances). Let students make choices about how they learn, and if it includes video games, so be it. My 13 year old self, and perhaps some 13 year olds in your class, will thank you.