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 with similar business purposes. They are a great way to keep your Microsoft 365 environment organized and let you set a custom inactivity threshold for each 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.