I downloaded elementary OS a few minutes ago. I really like it, but when I open the Software Updater and download its updates, I thought I saw "Elementary 14.04". I know elementary is based on Ubuntu and this might be silly but I'm scared. Will this change my computer to Ubuntu?
No it won't turn into Ubuntu :)
The updater will only update packages that you have installed, such as applications or your base operating system. Updates will fix bugs and add new features, but it won't ever install different software unless you specifically request.
Freya might have been confusing because it used Ubuntu's Software Center, but that has been replaced separately in elementary OS Loki (the Freya update) and in Ubuntu.