You have heard of the Rite of Econe. It is the 1962 liturgy with bows toward the Cross, St. Joseph in the Canon, the Confiteor before Communion, perhaps birettas in the sanctuary, and, in some daring places, no kneeling at the prayer for the Jews on Good Friday. This, not the 1962 typical edition, is what most traditionalists use as their base liturgy. But there once existed another usage of the 1962 Roman liturgy, one which was short lived and has since fallen into disuse: the Rite of Gricigliano.
Nowadays the Institute of Christ the King does 1962 with a few tweaks: Tenebrae in the evenings of Holy Week, violet during the Candlemas processions, proper doxologies during former octaves at the little hours of the Office, proper Last Gospels and commemorations, as well as the former ritual for solemn high Mass wherein the priest reads the lessons while they are sung. This is not the Rite of Gricigliano, but the rite of 1962 in the hands of Frenchmen. The Rite of Gricigliano is the old rite in the hands of a German.
When they began in 1990 in Gabon, the Institute of Christ the King was doing the pre-Pius XII Roman liturgy, as were most traditionalists outside of the FSSPX. Indeed, even many of Msgr. Lefebvre's independent allies used the old rite. This continued when they moved to their current house at Gricigliano in Tuscany. Their liturgy professor and master of ceremonies Abbé Franck Quoex assiduously taught and practiced the Roman liturgy with Pius XII's accession as the cutoff date, a praxis confirmed to me by a former rector of the Institute's seminary. The 1962 Missal was in the "hell" section of the library, with all the other books no one ever used. The Pacellian-Johannine book was be withdrawn from hell in case an astute jurist visited from Rome only to be returned swiftly to the folios and flames. Internal politics and the expulsion of a great number of priests caused for some changes within the Institute early last decade (a blog is not the appropriate place to discuss these issues). Around 2003, when a photographer took the photographs of Holy Week on this blog, the Institute ceased to use the old rite.
Rome decided to put all its traditional eggs in one legally uniform basket. The Pope, or those writing with his pen, resolved to place all communities using a pre-Conciliar form of the liturgy under the facies of the indult Ecclesia Dei and the pontifical commission of the same name. Fr. Wach was told to switch to 1962 and most of the Institute did. They were celebrating Holy Week according to 1962 by 2005 in most locations, but a few places held out with the inventiveness and ingenuity of a German priest within the Institute who did not obstruct the liturgical transition, but rather made it a process. Good Friday in many places saw the Gregorian Mass of the Pre-Sanctified celebrated, but with the administration of Communion—reserved on the credence table—during Vespers. Holy Saturday was done at the Pian times and with the Pian lessons rather than the ancient ones. The baptismal font would be blessed rather than a container of water during the Vigil and Pian Lauds replaced ancient Vespers. Thus was born the Rite of Gricigliano, a mix-and-match of the old and transitional forms of the Roman rite, a rite meant to transition from the old to the transitional! This went on for a few years. The oratory in St. Louis last celebrated the Rite of Gricigliano in 2008. I have heard of some celebrations in Europe that lasted as long.
As more communities reconsider their usages, the larger priestly groups are more entrenched in the Pian and Johannine years because of oversight. A diocesan bishop will neither know nor care about happened in 1956, but the local FSSP rector might! The Rite of Gricigliano lasted less than a decade. Now the Roman options of between the old rite, the middle rite, and the new rite.