It definitely can stay both at the same time. It's just that with huge volatility present, the people who are going to use it for payments is just going to be a minority; pretty much like the current state of bitcoin right now whereas pretty much only the people in the bitcoin/cryptocurrency community are willing to pay using bitcoin. With time(probably a lot of time), bitcoin should attain stability as more regulations come in along with market liquidity. This is one of the things that are just a matter of 'when'; then bitcoin can be used and owned widely for both store-of-value and for daily payments(assuming bitcoin is very noob-friendly at that time).