"Extract" v. "Extricate"

The meanings are slightly different; both are loosely defined as "to remove (from an environment)"; however, "to extract" is to remove something from its surroundings in general, while "to extricate" is to remove something from confinement, binding or difficulty.

So, it is possible to "extricate" something non-living, if it is in the context of removing the object from a confined space or to release it from bonds. You can "extricate" a fossil from the surrounding rock, for instance. You can, in almost all cases, use "extract" where you would use extricate, but not vice-versa. I say "almost" all cases because the term "extract" often has the connotation of removing something that is "mixed in", especially in scientific context. So, to "extract" a fossil from the soil might make it seem similar to the listener as extracting water from the soil. In political and tradecraft doublespeak, "extract" also has the connotation of placing someone in confinement, instead of removing them from it, making it nearly antonymic to "extricate".

Both "extract" and extricate" have the connotation of "to pull out." But the context is meaningfully different.

To EXTRACT something is to "pull out" something that belongs there NATURALLY. One extracts fruit juice from fruit.

To EXTRICATE something is to "pull out" something that has gotten where it DOESN'T belong. The mouse tried to extricate himself from the trap.