Social media data has become a crucial resource for understanding and detecting mental health challenges. However, there is a significant gap in our understanding of age-specific linguistic markers associated with classifying depression. This study bridges the gap by analyzing 25,241 text samples from 15,156 Reddit users with self-reported depression across two age groups: adolescents (13-20 year olds) and adults (21+). Through a quantitative exploratory analysis using LIWC, topic modeling, and data visualization, distinct patterns and topical differences emerged in the language of depression for adolescents and adults, including social concerns, temporal focuses, emotions, and cognition. These findings enhance our understanding of how depression is expressed on social media, bearing implications for accurate classification and tailored interventions across different age groups.