In Plant Database, for Crassula genus, something not fit on "Browsing by genus: crassula"
Here
http://garden.org/plants/brows...
appear: "Orostachys aliciae"

Here
http://garden.org/plants/brows...
appear: "Sedum (Sinocrassula indica)"

Here
http://garden.org/plants/brows...
appear: "Orostachys spinosa"

Here
http://garden.org/plants/brows...
appear: "Cactus" in the right of (Crassula pellucida subsp. marginalis 'Variegata')

Those plants (Orostachys and Sinocrassula) show up on the "Browsing by genus" pages for Crassula because they have synonyms of the Crassula genus. Crassula aliciae, for instance, is a synonym for Orostachys aliciae.

The fourth one in your list says "Cactus" because someone entered that as the common name for the plant.

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.