Both dalalat al-nass and analogy may speak of a rationale, but they identify and use it differently.
Dalalah: the prohibition of more serious harm to parents is grasped from the address “do not say uff” through its ordinary meaning and context.
Qiyas: a jurist identifies a legal rationale in one ruling and extends it to a distinct case through structured analogical investigation.
The source expressly marks dalalah as lughatan, la ijtihadan.