When they're saying top down or bottom up causation, they may be talking about emergence.
Bottom up causation is frequently another way to talk about weak emergence - how a high level macroscopic behaviour or phenomenon can be explained by (and in the best cases, even stimulated by) understanding the interactions of all the microscopic parts. An example of this would be something like quantum chemistry, where they hope to explain the behaviour of molecules by simulating the behaviour of the quantum elementary particles that compose that molecule.
Top down causation often refers to strong emergence, which is to say a high level phenomenon which isn't a consequence of the constituent parts behaving as they do, but rather the high level phenomenon theoretically has casual effects on its constituent pieces. This is a bit more speculative, in my view, and while I can't give you any known explicit examples, I can say they many people think consciousness is strongly emergent.
