Jes,

Excuse my ignorance, but by OP do you mean Dominicans?

This is because of different Mass formularies of the Sacred Heart - if one expands to the propers of dioceses and religious orders, there is further variation.

Up until 1929, there were 2 chief Masses of the Sacred Heart. They reflected two different historical emphases in the devotion. The Mass "Miserebitur" shows the origins of the devotion, as related to the "Passion" feasts, especially the feast of the Five Wounds (which was the first 'official' Mass of the Sacred Heart granted by a Pope). It was celebrated in red vestments, used (at first) the Preface of the Cross, etc. and generally reflected the themes of sacrifice, injury, reparation, etc. This was the Mass that was used when the feast was extended to the universal Church by Pius IX.

The second Mass "Egredimini" was granted toward the end of the 18th century by Pius VI (who defended the devotion against the Jansenists in Auctorem Fidei) to certain countries and dioceses. This Mass emphasizes the Heart of Jesus as an object of love, glory, thanksgiving, blessing, etc. It was celebrated in white vestments, used the Preface of Christmas [at that time also used for other feasts like Corpus Christi], etc.

In 1929, a completely new Mass with a proper Preface was promulgated under Pius XI, replacing the other two (aside from very few places which retained the Egredimini Mass). It was celebrated in white vestments but stressed the reparative-sacrificial element of the devotion, though it combined the themes of both Masses.

There are two other Masses that one can also find in the propers/appendices:

The first was used by some religious orders, especially the Eudists, and was composed by St. John Eudes: "Gaudeamus omnes" (the familiar introit, but adapted for the Sacred Heart). Like the Mass Egredimini, Eudes emphasized the aspects of the Heart as a symbol of interiority (a result of the French School of Spirituality also seen in the Sulpicians, Vincentians, LaSallians, etc.) and the adoration and thanksgiving to be paid to it. The second was the Mass "Venite ad me", which was used for a while, especially in the dioceses of France, also with similar themes.

ETA: as far as I can see, checking the Dominican liturgical books, the Mass Cogitationes completely replaced Egredimini, and so only Cogitationes should be used.