These 2 terms are not interchangeable, although reticent is occasionally seen in informal usage as an imprecise synonym for reluctant.
Reluctant refers to someone who feels or shows doubt about doing something, not willing or eager, or feeling or showing aversion. Synonyms are disinclined, dubious, hesitant, loath.
Dr Smythe was reluctant to share his preliminary, non–peer-reviewed research with the news media.
Reticent refers to someone who does not reveal his or her thoughts or feelings readily and is restrained in expression, presentation, or appearance. Synonyms are reserved, withdrawn, introverted, inhibited, diffident, shy, uncommunicative.
Professor Harrington has been described by colleagues and friends as “shy and reticent” but is also well known for his poise and calm demeanor during a medical emergency.
—Roxanne K. Young, ELS