Do people actually think this? ie. "it's not investing unless there's a chance of you making 10x returns"?

In my experience, it doesn't seem to be the chance of big returns, but rather the gut feeling of actively "doing something" to invest, vs. a very passive simple strategy of dollar cost averaging a low-fee broad index ETF. I think particularly in popular American culture, we often feel like it's more moral to actively make every penny, and have an aversion to passively earning money. Landlords are demonized, etc.

Yeah, this is bang on the money. And of course the financial institutions who make more money in fees when people are active vs. passively holding an index for decades, do what they can with marketing to support this idea.

"savings" implies that you can withdraw it at any time without loss, which definitely isn't the case with index fund investments. You should only "withdraw" in times of high market prices.

people see investments as something that returns 10x - so i say rather than calling index investing "savings", we should call the 10x type investments "speculation" or gambling.

I've literally never heard of anyone referring to index funds that way. You're not making any sense at all.

People don't refer to gold, or buying a house a "saving" either, but they definitely see it as safe haven values, and not as their money being "actively" invested (even as they do bear risks and are fiscally categorized as investments).

For people I talked to, beating inflation was their base goal.

I assume when people say savings they mean investments. Because it would be stupid not to invest a large cash position.

You would be surprised at the number of generally math-savvy (at least “enough”) people who have an irrational fear of “what if it goes down?” and fritter away decades of substantial growth (with each foregone decade skipping roughlh modeled as a missed doubling).

Savings accounts and similar are the appropriate place to put cash you’re saving for a specific purpose or for emergency funds. You don’t want to invest something you will or could need access to in the short term.