The cloud is not in the sky, it's somebody else's bunch of computers. A network within the internet.
if you have a bunch of computers, it's a network, within the Internet.
"the cloud" is a weird confusing marketting term.
So somebody else has a bunch of computers on the internet, accessible remotely over the internet, so as to provide some service, e.g. maybe a server to store your data on. Maybe some computers where you can create virtual machines on(a virtual machine - VM - elsewhere is I suppose known as a VPS - virtual private server, and you can SSH / remotely access a terminal - into it so it is a server in that 'listening on a port' sense). Maybe a server for your data, so you can remotely access your data and store it remotely. Maybe an application server (I saw one around 2005 before the term "the cloud" was around, called Citrix).
Before the term "the cloud", so many years ago, I remember somebody that had worked for some major tech company telling me the next thing was "the grid" , where people access computing services like we access electricity. That's probably the same concept as "the cloud". Though the idea of computer services being as simple to access and deal with as electricity is kind of a bit of a joke.
You write "By definition the cloud is offsite" <-- That word "offsite", just means not in your building. If you have a computer in your neighbours house then it's offsite, and if you connect to it with a big "network cable", or over WiFi, or telephone cables like the internet can be, then that computer is still offsite. offsite doesn't mean like "offline"!
Also, you could have your own personal cloud i.e. that you set up at home. And it's only then offsite in the sense that when you're not at home it's offsite. So, is a cloud necessarily offsite.. it should be accessible over the internet from elsewhere for when you are elsewhere.
The term offsite, let's consider, is it referring to you or the server. Probably the server(though philosophically, if the server is offsite from you, then you are 'offsite' from the server). And so it's suggesting that you are not near it. Well that's the case if the cloud is on google or amazon servers and you don't work at google or amazon. But if it's your own personal cloud then does the term "offsite" apply, if the server is in a location you frequently inhabit like work/home. So, I don't think the term offsite is good in defining what "the cloud" means, it seems too limiting, as you can have your own personal cloud and the term "offsite" wouldn't really apply to that. You can kind of bend the term "offsite" to say well it could mean that when you and the server are in different places..so, available when you and it are elsewhere, but it's stretching the term offsite.. the term offsite tend to mean somewhere else that you don't frequently inhabit. e.g. a friend's office, or google/amazon servers, not your home/work place. And you can have your own cloud at your home/work place with e.g. NextCloud. So I would take issue with the idea that a cloud has to be offsite.. but it should be accessible from elsewhere. The idea that it's offsite would normally happen to be the case for many people, because for most people it is, but not when somebody has their own personal cloud like NextCloud. (The other route you could perhaps take is to argue that NextCloud is not really a cloud, and NextCloud aside, one can have NAS. NextCloud is NAS but with a snazzy feature of being able to access documents in a web browser, and some other features). "The Cloud" is perhaps a marketting term to make it sound like these tech giants are offering something new, but really they are just taking control of your data with a view towards charging you for it! I may have to edit this again after a rethink, 'cos i'm not sure re the term offsite. It can be used in the term offsite backup.. so you have two backups, one local and one remote. Could be one at home one at work. So then a personal cloud is only offsite when you are in a location you frequently inhabit that is a place other than where the cloud is. So, does cloud mean offsite, still no.
So to your idea that a cloud is offsite, no. Or.. offsite is relative. So, is a cloud offsite? Offsite from another location, yes. Offsite backup is a useful term because it makes clear that you have 2 instances of the data. But otherwise what would you mean by offsite? Never there? That could be a meaning of offsite but from an IT perspective it's not a good thing, it's not a good or special thing or a useful thing. It'd be clearer to say you've let a tech giant store your data. There's no technical reason why your own NAS can't be called a Cloud. And if you think well they can offer some special features, well, so can you.
Really if somebody says they'll store your data and they tell you you can access it, and you say where is it. And they say it's "in the cloud", then they're probably a thief trying to pull the wool over your eyes. That's what the tech giants are doing. It's a savage baloney marketing term.
Offsite in the sense of offsite backup, fine, that makes sense it's a positive thing in computing, and offsite there doesn't necessarily mean a place you never go or a place you don't frequently inhabit. If you are going to use the term "offsite" for "the cloud" then you should define what you mean e.g. do you mean a place you never go. That's not inherently positive, it's not a technical concept, it's not a benefit in itself.
You write "all the network traffic to be routed to the cloud and back to the network again" <-- The cloud is a network. And your computer and the cloud are also on a network. So this doesn't mean anything.
