What are the similarities and differences between critical thinking and first principles thinking?

Let's put it this way: you can think of these two concepts as two different ways of "deconstruction."

Critical thinking is more like "finding flaws" and "quality inspection."

It takes an existing idea, an article, or a plan, and then begins to scrutinize it:

"Are your arguments sound? Is there any evidence?"
"Are there any flaws in your logic? Are you subtly changing the subject?"
"Have you overlooked other possibilities? Is there any bias involved?"

Its purpose is to evaluate and judge the quality, validity, and authenticity of something that already exists. It's like a product quality inspector, who takes design blueprints and standards to check if the manufactured product meets specifications and where its flaws lie. It is primarily outward-looking and defensive, helping you filter out unreliable information and preventing you from being easily misled.

First principles thinking is more like "deconstructing to an atomic state and then rebuilding."

It doesn't care what existing solutions look like; instead, it directly asks:

"What is the most fundamental problem we are trying to solve?"
"Regarding this matter, what are the absolutely certain, undeniable fundamental facts or laws?" (e.g., laws of physics, fundamental human needs)

It breaks down a complex problem into its most basic, core elements, and then, based on these "axioms" and completely unconstrained by existing frameworks, rethinks and constructs an entirely new solution. It's like a chef who doesn't follow existing recipes but instead considers at what temperature proteins denature, under what conditions sugar caramelizes, and how acids and oils emulsify. From these most fundamental chemical and physical principles, they then create an entirely new dish.

Therefore, their similarities lie in:

Both involve "getting to the bottom of things": Both require you not to take things for granted, not to believe everything you're told, but to question and delve deeply.
Both are deep thinking: Neither is a superficial way of thinking.

The biggest difference, however, lies in their "purpose" and "direction":

Critical thinking is "outward-looking," for "evaluation." Its object is external, pre-existing ideas and conclusions, with the goal of distinguishing truth from falsehood and making judgments.
First principles thinking is "inward-looking," for "creation." Its object is the problem itself, with the goal of starting from fundamental laws to forge a brand new path or solution.

To summarize simply:

When you see an article claiming "you must drink eight glasses of water a day to be healthy," you use critical thinking to ask: "Where does this conclusion come from? Is there scientific research to support it? Does it consider individual differences?" This is about evaluating an idea.
When Elon Musk wanted to build rockets, he didn't think, "How can I make existing rockets cheaper?" Instead, he used first principles thinking to ask: "What is the actual cost of the raw materials (metals, fuel, etc.) for a rocket? Why does it become so expensive when assembled? Can we organize production and launch in a completely different way?" This is about creating a new paradigm.

One could say that critical thinking helps you clear obstacles and deceptions from your path, while first principles thinking helps you find a brand new, perhaps even untrodden, path. Both are very powerful thinking tools, and they can often be used in conjunction.