Here is how I see the differences:
Constitutional party wants extremely limited involvement from the Federal Gov’t.—no involvement in guns, gambling, health care, schooling, taxes—basically Federal Gov’t should be very small and do everything we can to have unalienable rights. Government is mostly seen on a state level.
Democrats want the Federal government to be the basic regulatory agency. Government should direct social services and economic growth through policies, programs, and incentives. Certainly then taxes are necessary as they provide social services like education, roads, health care, energy changes, etc.
A Republican is between the two. I have not seen any Republican that believes in virtually no federal gov’t. Many want less gov’t and more reliance on the states to provide services. However, many republicans today also feel that they should direct social standards and impose morality codes on the states—to me that is not what a Constitutional party member would want.
Does that help?
Let me know if you need more.