The term "Constitutional Rights" is essentially a misnomer and/or shorthand. This is similar to the term "States Rights." States do not have rights - the term is just shorthand to refer to the powers that are retained by the state governments (i.e. powers that were never delegated to the Federal government).
Similarly, the term "Constitutional Rights" is shorthand to describe rights that are codified in the Constitution (inc. the BoR's). The point is that we do not have these rights because they are codified in our US Constitution. The US Constitution specifically limits the authority delegated to the Federal government...it doesn't "grant" any rights. The US Constitution simply codifies many rights that are (/were) already in existence/observed.
Unalienable Rights are rights granted to us by our Creator and/or observed in nature (i.e. Natural Law). These rights can not morally be taken away from us by an individual or government unless we have infringed on the rights of others. This concept is unbelievably important to understand...because the logical progression for pointing to our "Constitutional Rights" is that we don't have those rights if the Constitution doesn't specifically state them. THIS IS DANGEROUS and is the exact path that many DC'vers are taking with their comments and actions.
I'm going to speak on this topic on Saturday's show (3/9/13). Feel free to call in (or reply here, of course) if any additional clarification is needed.