If people prefer X over Y, that relationship would be "dominance": X has dominance. If X forcefully controls or overshadows Y, that relationship would be "domination". The ideas may overlap. Think, for example, of ...
"a dominant author"
...an author who sells more books than other authors
The author has dominance because people prefer his books, not because he has forceful control over them or the other authors.
"a dominant dialect"
..a dialect of a language has dominance if it is favored over other dialects by the population
..however, if people are forbidden or strongly encouraged not to use other dialects, that would be domination.
"domination by a monopolist"
If one company produces all the computers with no competition, that would be "domination".
"dominance of a favored producer"
If one company's computers are more popular than others, that would be "dominance".