Does Public or Private make a difference to Cloud Security?

When we talk about Cloud Security, the main concept is to separate, as an example, Coke from Pepsi. This implies that Tenant’s cannot impact the availability of each others data, the integrity of that data, and the confidentiality of that data. But what does this actually mean? Does this apply to all types of clouds in the same way?

There are three types of cloud families: Private, Hybrid, Public. There are at least 3 types of clouds: SaaS, PaaS, and IaaS. Do the same rules for one cloud family work for all cloud families? as well as for the types of clouds?

I believe the answer is yes.