Purpose tags and sensitivity tags are both used to label and apply settings to similar teams and groups, however:
Purpose tags are applied to teams and groups that have a similar business purpose. Purpose tags are a great way to keep your Microsoft 365 environment organized. Purpose tags also let you set a custom inactivity threshold for each business purpose.
Sensitivity tags are used to label teams and groups that share a similar level of data sensitivity. Sensitivity tags ensure that your teams and groups have the appropriate privacy, external sharing, and guest access settings. Sensitivity tags also let you set a custom external sharing review recurrence for each sensitivity level.
Training video: For more info, watch Purpose and Sensitivity tags.