A dispensation is a period of time during which God deals in a particular way with man in respect to sin and man’s responsibility. The word “dispensation” means “administration/stewardship/commission” and is first found in 1 Cor 9:17.
A covenant is an agreement or contract between men or God and men. (a man, a group, or a nation)
A simple analogy of the relationship of a dispensation and a covenant would be a game.
The dispensation would be like the time during which the game was played.
The covenant would be like the rules of the game.
In the New Testament the Greek word is found 33X. 13X translated Testament, 20X Covenant.