A depends on B if changing B may or tends to change A. (A given molecule's likely speed depends upon the temperature.)
A is determined by B if only changing B can ever change A. In that case, there is never a change in A not caused by a change in B, so B supervenes upon A. (Temperature is determined by the average molecular speed, it supervenes upon molecular motion. No change in temperature is possible without increasing the molecular motion, but some changes to molecular motion (one slows down as another speeds up) would not alter it.)
A is realized by B if every change to either makes a change in the other (because they are alternate descriptions of exactly the same thing.) (The temperature realises the ideal potential energy available -- they are different scales in terms of which to express the exact same thing, the former is just easier to measure.)
So each of these is a stricter requirement that the one above it.
So supervenient emergence allows for the idea that the more abstract phenomenon is really a separate thing with its own rules even though it arises out of the more basic phenomena -- data may be lost in the process of emerging, but that may allow us to make independent observations we could not see in the more basic phenomena, and that may alter the way the emergent concepts should be thought about or used. Supervenience physicalism holds that all phenomena supervene upon (or emerge from) physical states.
Realisation, rather than emergence denies there are two different things, or considers it irrelevant. So realisation physicalism asserts that everything really is physical (even mental states and idealisations like mathematical concepts) and that the separations we make between basic physical phenomena and emergent phenomena are arbitrary conceptual simplifications that we don't really need. In particular this eliminates the idea that the 'layers' of reality happen at relevant modal points (e.g. it indicates that the distinction between psychology and neurology is an arbitrary choice, and not a natural fact.)