My interpretation of cultural appropriation is where a demographic may claim or take over an aspect of another culture and this is done usually (though not always) from a position of privilege, be it by political power or brute force. Cultural exchange is where there is a mutual sharing, a give and take which does not strip either party of any trapping of its identity via conversion.
I am not sure what you mean by "take over" here. After a group comes to be dominated by another group brute force or direct state power(not sure if that was what you meant by political power) whether through laws or otherwise, need not be necessary for cultural appropriation to take place. Individuals from within a privileged culture have a power that those not privileged do not i.e they have the ability to affect how that culture is perceived and interpreted(as they are more likely get more attention), whose interest it can be directed to serve(as a group) etc. The need not be conscious of what they are doing. They are simply adopting and using these expressions of the group without being aware of their privilege and the implications of that privilege in their use of the cultural forms/expressions. They need not themselves claim that culture as theirs but their privilege makes it all the easier for it to be attributed to them or for them to become the most visible representatives of that culture. A good example is Eminem the self proclaimed "Rap God"....the dominance in both international Reggae and Hiphop charts of mainly white artists. The same took place with Jazz.
This idea of cultural appropriation is also confusing for me at the moment because I witness many instances of cultural fusions which in turn generate a new expression of identity separate from the original inspiration. Cuisine, fashion, even language. Isn't this also a form of cultural appropriation?
I would point to cultural appropriation as the terms on which a cultural expression is used at a particular point in time or over a period of time[I explained the terms above]. It need not and usually does not have absolute or permanent effect. What I mean by this is, first, the fact that a privileged group has appropriated a cultural expression of the other group does not mean that that other group may not continue to use that expression and continue developing it on their terms(though often less visible) or that segments or members of these groups cannot engage in mutual sharing. There are good examples with many African musical expressions like Jazz, Rock and Roll and Hiphop. However many people know of these forms from the perspective and expression of whites.
Down the line these groups may come into development of expression that may more resemble(or reflect) a mutual sharing or more equitable terms of interacting, so cultural appropriation is not something that necessarily has effects of a perpetual nature.
https://www.youtube.com/watch?v=az3NAoVInQQ