There’s some good info about dedicated servers here:
Generally if you want to rent a server you will want to google ‘dedicated servers’, or if you want to buy your own server and have a datacenter host it for you you will want to search for ‘co location’.
I would say most people opt to rent, as the hardware is covered by the company. If you co-locate, any issues with hardware must be sorted out by yourself or by paying the datacenter.
The funny thing is years ago the best option and the most expensive option was dedicated servers (as opposed to cloud). I personally feel the best option is still dedicated servers, but nowadays, it’s actually cheaper than cloud - if you are spending over $100 a month. However, it does involve more set-up and maintenance - as you do it all yourself (it’s almost become a bit of a lost art - as not many people run their own servers now, at least not as much as before).
