That really depends where you are purchasing them from. There are multiple places you can buy them from, and some will stream the files live, some will allow you to download them for offline use and some places will offer both.
For eBooks, most services allow you to download the ebook file to your phone. Personally, I've used three ebook apps: Google Play, Amazon Kindle and Kobo store. Amazon and Kobo download the full book the first time you read them and work offline just fine. Google play ebooks normally streams books via your data connection but allows you to download files for offline use (just make sure you remember to do this before you turn off your data connection).
I've never tried purchasing movies on my phone before, but I think your best bet would be to check the FAQ of whichever service you're going to buy them from and see whether they offer streams or downloads.