A semi-dedicated server is often just a large reseller account. You will probably get about 15-20GB space and a few hundred GBs data transfer. There will probably only be 3-5 of these type of accounts on the server, however each of these users will most likely be able to have their own resellers and accounts in their space. Your host will take care of all hardware and software management. It is a good step up from a smaller reseller account before moving onto your own server.
When you do reach your own server you will be the only one on it, you will get overall root access and can do what you want in terms of software and what plans you setup.