Not quite. I'm not really sure but I think the original idea actually was a fixed hardware address but I'm not sure if a lot of devices actually ever implemented it that way because it's simpler (and cheaper) to control it in software. In modern (especially mobile) devices it's actually a security requirement because with a fixed MAC address you could be tracked by other wifi devices.
As the others said that is normally the case but nowadays most computers and mobiles have an option that randomize the MAC addresses on each connection.
These MAC addresses are known as locally-administered address.
They look like this: