Thank you Zuzu.
I do not know how it would be better for cases of synonyms. Maybe the way it is now.
About using the common name "Cactus" for other species that don't belong in Cacti family, I think it would be desirable to avoid this.
The source of this common name applied to other succulents might be the labels of some nurseries. I saw frequently displayed as "Cactus collection" different succulent plants that do not belong to Cacti Family. Or the source can be the internet. Frequently the word "cactus" is misapplied.
But there are not rules in establishing common names of plants, so nobody can deny if it's incorrect or not to use a particular common name.