Which word indicates that things are entirely dissimilar?

The term "disparate" conveys the idea of things being fundamentally different or having no similarities. It is often used to describe items, groups, or concepts that are entirely unlike each other in character or nature. The use of this word implies a complete separation between the entities being compared, emphasizing their lack of shared qualities or attributes.

In contrast, the other options relate to different themes. "Dissonant" generally refers to a lack of harmony, typically in music or sound, rather than a direct comparison of dissimilarity. "Disengaged" implies a state of being disconnected or removed from something, which does not inherently capture the essence of dissimilarity between things. "Distinct" means clearly different, but it does not necessarily imply that the things are entirely dissimilar; rather, it can indicate that they have unique attributes while still having some similarities. Therefore, "disparate" is the most accurate choice for indicating complete dissimilarity.