Does "Being in schism" merely imply mutual excommunication? (Catholic perspective) In the answer provided to the following question:
Explanation of the bell, book, and candle ritual of excommunication the author states that it is a common misconception that excommunication implies someone has been kicked out of the church, it merely means that they have been barred from the sacraments. In other words someone who has been excommunicated is still part of the church.

I was wondering how this applies to large-scale excommunications, such as the great schism, where the West excommunicated the East and vice versa? Does this mean that the West and the East were actually still the same "undivided" (in a sense) church, but that the West considered Eastern Sacraments illicit and the East considered Western Sacraments illicit?

I ask because this would have interesting consequences for ecclesiology: From the Catholic perspective, other Christian bodies are still within "the one true church", however they are "excommunicated" which simply means that they are barred from the sacraments. In the case of the Orthodox churches, their sacraments are valid, but due to their "excommunicated" status they are illicit.

If this is true, it actually puts my mind at rest in terms of the whole "we are the one true church" position that both the Eastern Orthodox and Catholic churches hold, because it allows them to both be correct: there are not two Churches claiming to be the one true church, there is only one, but there are excommunications at play within it that make it seem as though there are two (or more)

Scoping this to Catholicism.

PS: Potentially the word "anathema" has some role in all of this. Is an anathema different to an excommunication? Does receiving an anathema imply that you have been kicked out of the church?
It is important to note that when we speak of the "schism" between the Catholic Church and the Orthodox Church that began in the 11th century, that it was not the first time that the Orthodox Church was out of communion with Rome.  In fact, the division was seen as completely reversible until the pillaging of Constantinople during the 4th crusade.

The word "schism" in my mind conveys a sense of permenance and or/finality.  In this sense, I feel that the Great Schism only acheived the status corresponding to its name after no viable path to reconciliation appeared possible.