I didn't think drug enforcement was a duty of the Coast Guard. Usually anything related to cargo and crew is the CBP's responsibility, while the Coast Guard is about safety (life-jackets and -boats, certifications, search and rescue, etc.).
The USCG has several sets of classes of ships, informally known as black, white and red hull. Black does what you say, white does border patrol for drugs and people illegally entering the country, and red is scientific and icebreaking. See http://www.uscg.mil/proceedings/spring2011/articles/10_Tlapa...
Looks like there's a wide swathe of "homeland security" missions on top of the more traditional missions I was aware of, deemed "non-homeland security":
Around here, Southern California, the Coast Guard regularly does drug interdiction duty. The boating safety stuff is usually done by the Harbor Patrol/Sheriff's Department.