There are ETFs that follow an index. Let's say the classic S&P 500. We have two different ETFs following the same index. Let's say Vanguard and Schwab. Let's say Vanguard has much higher demand for some reason in a time range of 1 year. Will this 1 year the Vanguard ETF go up much faster than the other one even if they are following the same index?
No, this would create an arbitrage which an authorized participant (AP) would quickly take advantage of. Worth reading up about the creation and redemption mechanism (here is a good place to start) to understand the exact way this happens in ETFs as it's very key to how they work.