I think that in that context, investing means putting money back in circulation. For example you invest in a company and that money goes to pay providers, salaries, taxes, etc. It gets back into circulation straight away. But I don't think that's the case with most stocks and ETFs, most of that money just circulates in the stock market for speculation, maybe a small part of it goes back with comissions and brokers and taxes, but it doesn't do that much good in the overall economy.

>save money in the bank

This money is effectively lent to the bank, which will then re-lend it. A small share to the Federal Reserve, the rest to mortgage holders, businesses trying to meet payroll and so on.