HPSP is a scholarship from the Army, Navy, or Air Force that pays full tuition, books, and fees, while giving you a stipend of $1,992 per month. You simply go to school like every other student, but must do a 45 day active duty rotation every summer (unless your school's schedule does not allow for that). A 3 year scholarship will obligate you to 3 years of active duty upon graduation. Additionally, you can take a $20,000 signing bonus that obligates you to 4 years served concurrently with your scholarship obligation. Upon graduation you will be paid as an O-3 with <2 years service, plus BAH, BAS, and dental special pays.
HSCP is a Navy program. It is not a scholarship, and does not pay for tuition, books, and fees. It simply places you on active duty while in school with a paygrade of E-6 (with ability to promote to E-7 if certain provisions are met). You will be paid as an E-6 with <2 years of service (which will increase upon gaining years/promotion to E-7), plus BAS, and BAH. Your only obligation while in school is to pass a physical fitness test every six months. Your active duty time in school counts toward retirement and for pay purposes. Upon graduation, you will commission as an O-3 with however many years of service gained while in school, plus BAH, BAS, and dental special pays. Taking a 3 year HSCP will obligate you to 3 years of active duty after you graduate.
The National Guard program Smills91 was referring to is the Medical and Dental Student Stipend Program (MDSSP). You join the Army National Guard (or Army Reserve) as an O-1, and receive a stipend of $1992 per month in addition to your drill pay. The program does not pay your tuition. After graduation, you will be promoted to O-3, and will owe 2 years of drilling with the Guard for every year you spent on MDSSP. You are non-deployable during dental school and also during residency if you choose to do one. There are additional programs that you can take after you graduate for an additional commitment, such as retention bonuses, student loan repayments (HPLRP), and a stipend during residency (STRAP).