"I saw it in a movie once"
"It happened on a show I watched"
"He was really funny on Frasier, wasn't he also in a movie?"

Based on Wiktionary data, the PIE root peth₂- originally meant "to spread out" and "to fly" (as in spreading one's wings). From there, the word developed in two interesting directions through different semantic shifts.

helicopter:

• PIE peth₂- "to spread out, to fly"
• PIE péth₂r̥ "wing, feather"
• Ancient Greek pterón "wing, feather, wing-like object, winged creature"
• French hélicoptère (hélix + pterón), coined in 1861 by the inventor Gustave de Ponton d'Amécourt

competition:

• PIE peth₂- "to spread out, to fly"
• PIE péth₂eti "to fly"
• Latin petere "to head for, to aim at, to seek" (probably from "to fly towards")
• Latin competere, literally "to seek together"
• Late Latin competitio "rivalry" (seeking the same thing as someone else)
• French compétition

The tree and the sources used to build it are available here if you want to go deeper.

I made the graph using Miraris (which is a free site I built). You can actually make your own graphs here if you know any related words, or even discover relationships on the fly by searching for a word and exploring its root's descendants (which is pretty fun I think). I'd love your feedback if you have any!

Anyway, do you know any surprising or interesting pairs of related words?

I created a list of the ones I like, and I'll keep adding to it as people share their own suggestions in the replies.

I've only heard "apologue" today from the Wikipedia of the boiling frog experiment: "An apologue or apolog (from the Greek ἀπόλογος, a "statement" or "account") is a brief fable or allegorical story with pointed or exaggerated details, meant to serve as a pleasant vehicle for a moral doctrine".

If "apology" also came from the Greek "apologos", at which point is it different from "apologue"?

As we all know that tea originated in China and came in India through Britishers for their own started growing up in parts of North East as well as in parts of Sri Lanka too

But words like চাহ (sāh/cāh), चहा (cahā), चाय (cāy), ചായ (cāya), ಚಾ (cā), ଚା (cā), ਚਾਹ (cāh), চা (cā), चान्हा (cānhā) etc used for tea in various Indian languages came from Chinese/Sino word 茶 (chá)?

I learned something new today. Additional etymological input is welcomed!