Yes, and then some. NIST 800-145 basically defines cloud as scalable, ubiquitous access to network resources (in addition to the 5 characteristics). That said, cloud typically carries 4 defined (or recognized) deployment models: private, public, hybrid, and community. Technically any deployment model can be on or off-prem which brings us to defining capital expense vs operating expense - do we buy the physical boxes and infrastructure, plus FTE to configure and maintain or do we just 'rent' space and scale as we need. The Total Cost of Ownership (TCO) really needs to be defined to know what is better aligned with the goals of the organization.
That said, if you host everything on-prem, best to have a off-prem cloud backup for BCDR (business continuity/disaster recovery) and if we host everything in an off-prem cloud, best to have a backup in a separate cloud in a different availability zone - TCO can get really tedious really quick.
Good points about TCO being something a company needs to assess for themselves, rather than "cloud is always cheaper" or "on-site is always cheaper". It's not my field but I'd hope there are approaches that let a company first use the cloud to figure out how much they really need, then later switch to on-premises and not have to reconfigure things (i.e. they can have their machines present the same cloud interface).
approaches that let a company first use the cloud to figure out how much they really need, then later switch to on-premises and not have to reconfigure things
There is. As an org seeks out a cloud solution, they will meet with a sales engineer and/or a solutions architect to complete a 'right-fit' type interview - costs for a length of time will most likely be discussed at that time. Of the 'big 3' (AWS, Azure, Google), AWS does offer a 'free tier' for one year for some services if one knows what they want upfront - I can only speak to AWS on the free tier thing. During this time, an org could build out the environment they want to mimic what they get in the cloud and use a method called 'forklifing' their data right back into their own environment - best to run operational tests here before any divestment decisions!
Before all of that though, the org needs to ensure no vendor lock-in for services (meaning the org cannot operate without that service that is wholly owned by another entity) and the org will need to honor any length of service - whatever is defined in the Statement of Work (SOW) and/or any other contractual documentation, lest they face a penalty - such as buying out the term remaining, etc.
Personally, I think medium to large cloud environment are best fitted to medium to large enterprises, especially those that are decentralized and for e-commerce that require traffic bursting scalability.