'Resting', in both natural language AND 5E RAW, is 'avoiding strenuous activity'.
If we assume that the definition for "rest" used by the game is the natural language definition, that raises a question; What is the purpose behind the author saying the following?:
"They need rest - time to sleep and eat, tend their wounds, refresh their minds and spirits for spellcasting, and brace themselves for further adventure." instead of "They need rest."
"A short rest is a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending wounds." instead of "A short rest is a period of downtime, at least 1 hour long."
"A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours." instead of "A long rest is a period of extended downtime, at least 8 hours long, during which a character can sleep. A character can also stand watch for up to 2 hours during a long rest."
So, RAW, there are not two different types of inactivity!
You are missing the forest for the trees - I am not talking about how many types of inactivity there are (which, by the way, it's strange to call what the book calls "light activity" "inactivity" because those words are not synonymous). I am talking about how many game terms or elements the rules present relating to rest, and that number is 2 - Short Rest, and Long Rest - which is clear because each gets it's own paragraph heading in large, underlined text.