Specifically as used by the Reformed theological tradition, what is meant by the term "covenant"? How is this different than other forms of agreements under assorted names in English like contract, agreement, pact, pledge, etc. How should the term be understood when used as an adjective, such as in "covenant theology"?
Before getting to the specific difference you asked for, I think it's necessary to understand the various ways in which the term is used - particularly the legal definition. In Reformed theology, the relationship between God and His people is often couched in legal terms, particularly in relation to Covenant Theology.
In browsing all of the various definitions, the distinction appears to be generally a level of solemnity, where a covenant is a type of contract that is considered solemn.
In the legal definition of a covenant, this note is included:
Another phrase that came up in all of the definitions for the various types of covenant is this:
This is very similar to the definition of a Biblical covenant, where the covenant is between God and His people. I believe that this is also the Reformed theological traditions that you specifically asked for. Example (one of many):
2 Chronicles 7:14 (KJV)
Many reformed theologians would begin a discussion on the topic of covenants with the way they understand the biblical covenants to be formulated. God uses language and objects we understand to relate His truth to us. Many Reformed theologians also believe that he used a covenantal structure called a suzreinty vassal treaty which was common among the Hittites at the time of Moses, to structure His covenant with His people so that they would better understand what he meant by it.
A SV treaty has a specific form and purpose which is well explained in the link above and this has a very high level of similarity to the Book of Deuteronomy and other parts of OT scripture.
The important issue here is that there is a distinct difference between this treaty or covenant and a contract. A contract is entered into by two (or more) parties who both come of their own free volition and they are generally at an equal level as they sign the contract. In sharp contrast with this is a SV treaty where the suzerain has either conquered or come to the defense of the vassal and imposes the structure of the covenant on the vassal.
On the other side, the suzerain not only imposes his will but also binds himself with duties toward the vassal. So basically it was something like this: I (suzerain) delivered you from your enemies, therefore you (vassal state) will pay me tribute and you will send men to serve in my army every year. In exchange for this I vow to defend you from your enemies.
Many Reformed theologians believe that the covenant God has made with His people is of a similar structure: I created you and even though you rebelled against me I sent my Son to die for you. I have conquered your enemy the Devil and will continue to defend you from him. Therefore you will serve me and offer me praise.
Reformed theologians believe that God has created this sort of a covenant with His elect people unilaterally, and that we only love God, because He first loved us and imposed His gracious covenant on our rebellious hearts.