TL;DR: The "Cloud" is just a different term for the internet.
In networking lingo the Cloud was always used as a representation for the internet. Compared to other types of networks like local area networks (LANs) the internet is displayed as a cloud symbol in all networking diagrams.
At some point someone used phrases like "send data to the Cloud" or "store XYZ in the Cloud" for marketing purpose, and this is most likely how it started. The term hasn't any impact on the process of how you store and retrieve data from the internet. It just sounds more modern.
The services of the Cloud
Since Cloud means internet there are many services which you can use nowadays, like data storage for example. There is a vast offer on Cloud storage providers, like Google Drive, Dropbox, WeTransfer, etc. Some are with certain use cases like short term file exchange of large amounts of data (as WeTransfer offers), or long term storage that can be used for archiving (Google Drive).
These possibilities have been there since the start of the internet, but were mainly used by enterprises to have their data available for all subsidiaries, especially if they were located all over the world. It was with this new marketing gig, called Cloud to have these services available for everybody and even accessible on every device.
Another service in the Cloud is called "Cloud computing". This is where big brands like Amazon came into play, not just for shopping. We'll talk about this in another post.
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