Between different attributes in CBC, they should be as unrelated as you can make them. But, in reality, there are many attributes in CBC that will have some relation in respondents' minds (such as style and color; or brand and price sensitivity). The experimental designs you use (that CBC software automatically generates) should show each level almost exactly an equal number of times with every other level. In that sense, the attributes are shown in a non-correlated way to respondents. But, respondent preferences for combinations of levels between attributes (such as style x color; or brand x price) may lead to synergies or dis-synergies, also known as interaction effects. When that happens, you can include interaction effects in your models to capture those synergies and fit the data better.
As for MaxDiff, typically no interactions are modeled. Each item shows an equal number of times with each other item. But, many items included in MaxDiff can be related. For example, for a study involving job satisfaction elements, the three items: 3 weeks vacation, 4 weeks vacation, and 5 weeks vacation might be included in the total list of items. Obviously, these items are related to one another. But, the independent utility of each can be estimated. Interactions are not typically estimated in MaxDiff experiments.