It's somewhat of a mindset question and somewhat of a wealth question.

Mr $300k may have zero months in an emergency account, but be stable in his job as a doctor and not worry about finding work - and may actually "feel poor" because he barely has any "fun money" to waste and feels he can't buy coffee in the morning.

Mr $40k a year may have 6 months of expenses in the bank, saving half his income to FIRE, and know that anytime he wants to he can buy that coffee - and sometimes he does.

Net worth likely says Mr $300k is worth more than Mr $40k - but that may not be true forever, and Mr $40k may be "retired" at 50 while Mr $300k is perpetually working until death.

Who is rich, who has wealth, and who is happy? There are no clear answers.

You're missing the third question which is of definitions. There's an other person Mr $65k who after all their necessary expenses has $1k left over each paycheck that they spend on dinners out, concert tickets, vacations, etc so that at the end of the month they are left with no additional savings. Are they living paycheck to paycheck?