“I cut a branch from this tree” describes an actual physical separation. “From this man I draw an intimate friend,” when referring to that very man's intense loyalty, is an imaginary and rhetorical extraction.
The shared idea of “from” or min does not decide the classification. Tajrīd requires a counterpart similar in the same relevant characteristic and an intention to intensify that characteristic.
An ordinary act of extraction may correctly be called extraction in language; it is not for that reason automatically the semantic figure called tajrīd.