Am I right in saying that a Critique is not just stating your opinion of what is good and bad, but trying to back up the opinions as well?
That's kinda putting the cart before the horse. You aren't trying to back up opinions (which are subjective). "You're ugly! And, uh, *quickly googles up some out-of-context 'facts'* here's evidence so I can win the argument!"
I don't know much about painting, so I look at a painting and say, "I don't like it, it feels weird, and the colors clash too much, but that pattern on the guy's clothing looks cool."
An artist looks at the painting and says, "Your perspective with this object doesn't match that other object, the shadow there doesn't actually line up with that light source, color A shouldn't be paired with color B because of (color theory magic), those stones look too clean."
It's not trying to gauge quality/worth, it's trying to examine flaws, as a fellow creator, that'll be useful to help the creator improve the work.
Reviews say, "The game is good, here's what I liked/didn't like from the perspective of a consumer, based on my tastes."
Critiques say, "As a fellow designer, here's what you need to remove or improve, based on my experience and knowledge."
Reviews are usually (but not always) more geared toward other consumers, to give other consumers more information to make an informed buying decision.
Critiques are geared toward the developer or other developers, to help improve each other's craft.
Because there is some overlap (they can both be feedback, or they can both not be feedback), the words occasionally get used interchangeably.
Another subtle distinction is that reviews are saying what's good/bad, critiques are saying why it's good/bad.
Here's a quick review of a single screenshot - it's me speaking about what I'm feeling, as a consumer.
Here's a critique of some game mechanics - it's me debating (with explanations) about why I think that's not a good idea, as a fellow creator.
Here's a review of a single music track - it's me speaking about what I'm feeling, as a consumer.
Here's a critique of laying out game worlds - it's me explaining what I think is wrong with the poster's current approach, and what I think a superior approach is, as a creator.
All four of these also happen to be feedback directed at the original creator to help them improve the work, but reviews and critiques can both just as easily be directed at other consumers or other creators. For example, one designer might critique a game to help other designers (not necessarily the original creator) learn from its strong-points and flaws.
Another example is, a few months ago, I was proof-reading a friend's book for them. Not being an author myself, I was reviewing the story as a reader, to give the author feedback on what I thought of the story, and offering suggestions and opinions on the descriptions, sentence-flow, and overall plot. At the same time, I was also critiquing the author's punctuation, grammar, and spelling.
