Deecon, to answer your questions... yes a graphics/video card is the same thing.. just different terminology...
The Intel(R)82865G Graphics Controller is a ten-cent chip built onto your motherboard (the main circuit board for your computer) and to be honest with you, I'm surprised that it has even been running aces high at all! Yes, it is THAT POOR of a performer! It was designed to play games like solitaire and get you on the internet.. and that's about it.
There are three types of 'slots' that separate video cards will fit. In the real old days, it was PCI. The next generation of computers used what is known as an AGP slot, which is much faster and more capable than PCI slots. The latest (and currently used) slot for video cards is known as PCI-Express (shortened to PCI-e), and is many many times faster than AGP. It would be difficult for me to go into details as to why these are called what they are and how they work, just remember that virtually all new systems built/sold today use the PCI-e standard of video card. AGP's are getting harder to find and more expensive because of that, and the old PCI video cards are all but non-existent now.
Also keep in mind that as video cards have progressed throughout the years, so have their power requirements. Since they do more things at faster speeds, they require more power. This is a big reason why the power supply on your computer won't likely support any newer video cards at all.
You mentioned having an old Dell, so depending on how old it is it could theoretically be any one of those three slots but Dell has been around for quite awhile. Simply put, we need more information about your computer before we can even begin to tell you what you need. A model number would be great. If you can't find that printed on a sticker somewhere, how about at least letting us know exactly how old it is?
I'd hate to say it though, but given your lack of experience with computers you might be better off just buying something new.. that is if you are financially able. It doesn't take a real expensive system to run Aces High quite well, especially if you can do some research and if you're willing to learn how to build it yourself. Also, it often doesn't make a whole lot of sense from a financial aspect to try to upgrade an old, aged system (if it can be upgraded at all) when for just a little bit more money you can usually replace it with something much better.