A ‘rite’ is the way a particular celebration is to unfold. For example the Rite of Baptism contains everything for the celebration of baptism in the order in which it is supposed to happen: the greeting at the back of the church, the questions, the actions, the prayers, the intercessions, everything from A - Z.
In most ‘rites’ you will also find ‘rubrics’. Rubrics are usually written in red ink and tell the priest what to do: i.e. “the priest genuflects” “the priest shows the Host” “the priest makes the sign of the cross”, etc.
Rubrics - Among the ancients, according to Columella, Vitruvius, and Pliny, the word rubrica, rubric, signified the red earth used by carpenters to mark on wood the line to follow in cutting it; according to Juvenal the same name was applied to the red titles under which the jurisconsults arranged the announcements of laws (more info here: newadvent.org/cathen/13216a.htm)
No they are not the same. A Rite is an official Church liturgical process. The Rubrics are the words that are printed in RED in the official liturgical books that are instructions to the Minister on how to do certain things.
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