Recent findings have shown that mind-wandering - the occurrence of stimulus-independent and task-unrelated thoughts - is associated with negative affect and lower psychological well-being. However, it remains unclear whether this relationship is due to the occurrence of mind-wandering per se or to the fact that people who mind wander more tend to be generally less attentive to present-moment experience. In three studies, we first validate a French translation of a retrospective self-report questionnaire widely used to assess the general occurrence of mind-wandering in daily life - the Daydreaming Frequency Scale. Using this questionnaire, we then show that the relationship between mind-wandering frequency and psychological distress is fully accounted for by individual differences in dispositional mindful awareness and encoding style. These findings suggest that it may not be mind-wandering per se that is responsible for psychological distress, but rather the general tendency to be less aware and attentive to the present-moment. Thus, although mind-wandering and present-moment awareness are related constructs, they are not reducible to one another, and are distinguishable in terms of their relationship with psychological well-being.