I'm not sure how to ask it. Is something like OpenStack the same thing as AWS and Azure, except it is Open Source? If I wanted to create an onsite cloud for a Production environment, can OpenStack (or other) be used?
Generally yes - all of them are large ecosystems of related software products working together to implement "clouds".
There won't be an exact 1:1 mapping for each and every one of their individual products, features and APIs, so don't expect that. But there is a quite significant overlap in capabilities and functionality in general. Just like with the public cloud providers: they're similar to each-other, but not exactly 1:1 compatible.
You (and your customers) will have to learn the specifics of using the desired cloud products in the ecosystem, just like with the other cloud infra providers.
But you'll also need to learn how to install, maintain and operate the infrastructure in general as well as the individual products you're gonna offer, which is something users of the public cloud providers don't need to worry about.
In the cloud theory there 's 3 types of cloud : Public Cloud, Private Cloud and Hybird Cloud
Openstack one kind of the private cloud, the alternative is opennebula and cloudstack
And Azure, AWS and GCP is kind of Public Cloud Service
And the hybird cloud is the cloud that combine 2 of that type of cloud