On ETH Gas Station it says that the standard cost for transfer is ~$0.06 currently but when I send ETH on metamask I could't set the gas limit lower than 21000 which is roughly half dollar (10 times more than what ethgasstation says). Why is there such a big difference?
I think you're confused between gas limit and gas price.
The gas limit is the maximum amount of gas that can be consumed by your transaction. (21000 is actually the smallest amount of gas that a transaction can use, so you'll never set the limit lower than that.)
The gas price is how much ether you will pay, per gas consumed, for the transaction. The overall cost of the transaction is thus
gas consumed * gas price. At the moment ETH Gas Station says a standard gas price is 4 gwei, so that's a good figure to put into MetaMask. At current prices,
21000 * 4 gwei should cost about $0.06 USD.
MetaMask may very well suggest a higher gas price, but you can (and probably should) just change it to be more in line with what ETH Gas Station suggests. Just make sure you're changing the gas price, not the gas limit (or "units" in some UI).