Was bitcoin designed to provide both functions, or just one? How does it mainly function today?
Today, it primarily serves as a store of value. It is inherently more useful as a medium of exchange, its intended purpose. Perhaps a bit ironically, its expected future usefulness as a medium of exchange is what is driving its present usefulness as a store of value. The thinking is that if you get them now when they're cheap, in the future when they're used as a medium of exchange (and thus there's much more demand) they'll be worth more.
Today, due to relative low acceptance rate, it doesn't fulfill it's role as a medium of exchange anywhere near potential. Instead the largest amount of transactions is, as with regular money, people speculating on it's future value.
It's important to look not at what it's meant to be, not at what it is, but how it works out for people. Occam's razor applies rigorously, the way something works is how it works for you. Don't complicate it.
In the near future it can be used interchangeably with any currency. The question of whether or not it is one is therefore irrelevant. It will be the only currency-like to be safe, certain, quick and cheap all at once. Let's not argue syntax, let's argue semantics.
When I use bitcoin as a medium of exchange I have to be confident that the bitcoins will not change in value between the point I receive them and the point I spend them.
Not really. Most methods of money exchange or transfer bear some costs or risks. Credit cards, for example, require fees (which are paid by the vendor of a good). If the price flictuation of bitcoin which happens during a transaction is small enough that it is more economical to use them than, than to ise other means, they are cheaper.
The duration of a transaction - that is, the time span between a buyer sending an amount and the vecdor beoing able to re-send that to an online monex exchanging services which pays that to his bank account - is around one hour. As credit card fees and costs are easily in the range of 5 % of a traded price, any volatilty which is less than that would still result in more economical transactions. However, quick changes om price are harder to handle - it is far more comfortable if the buyer can acquire his coins a few weeks in advance and the seller has several weeks of time. This a lower volatility is more comfortable for that.