All of these blessings share a common formulation: "Barukh atta HaShem" - blessed are You, HaShem. Despite this common linguistic structure, there seems to be a fundamental difference between the first three categories (enjoyments, mitzvot, and praise) and the last category - blessings of prayers. We see for example that when the Rambam explains the structure of blessings in the laws of blessings (11:1) he mentions only the first three categories. The Zohar also states that there is a fundamental difference between the blessings of prayer and the other kinds. (Zohar Ekev III:270b-271a.)
Here is one way to understand this difference. In both kinds of blessing, we are striving to testify to the connection of the physical world with the world of holiness and G-dliness. Rav Moshe Cordovero writes: "Every physical act needs to be accompanied by a hidden, spiritual aspect; and that is the essence of a blessing on a mitzva so that the physical action should be accompanied by the spiritual aspect namely the breath of speech, and above that the thought which gives rise to this speech" (cited in Yedid Nefesh commentary). We can easily extend this idea to blessings of praise and enjoyment. In all of these cases, the material subject of blessing is already before us: the mitzva act (for example, lighting candles); the object of praise (for example, a beautiful landscape) or the object of enjoyment (for example, a piece of fruit) are before us. Our job is to testify to the connection of these material acts of objects to the world of holiness: the act is connected to holiness because it is a commandment of HaShem; the object of praise or of enjoyment has this connection because it testifies to His beneficence.
In these cases, we are called upon to relate to the existing physical reality and connect it to holiness. The material is present, but the spiritual dimension needs to be provided by the blessing.
However, in our prayers we are asking HaShem to answer our requests and transform the existing physical reality. In a way the situation is exactly opposite. We stand in prayer before G-d; our entire experience during prayer is one of complete holiness. What is lacking is the material dimension; we ask HaShem to provide wisdom, livelihood, redemption, and so on.
The common denominator of these two kinds of blessings is the word "barukh", which describes an inner connection between the worlds of matter and spirit - a connection which the Jew is constantly working to strengthen. The Jew does not move back and forth between the disconnected worlds of material and spiritual, at one time eating an apple and enjoying a landscape and later on escaping into a detached meditative prayer. Rather, we are the go-betweens between these two domains. Any time we are involved in the world of action, we are striving to establish and strengthen the influence of holiness. Anytime we are in involved in the world of prayer, we are striving to create a physical world which is in a suitable receptacle for such holiness.
In each case, we testify that HaShem is "barukh", blessed, for He is the Holy One yet His holiness is expressed and accessible in the material world through uplifting experiences and through the holy acts of the commandments of the Torah.