Right - VGA is the older style connector - DVI is the newer style. For DVI to work it's needed on the graphics card and the monitor. Normally ony higher spec TFT screens have DVI inputs, though it's becoming more common.
Use of an adapter negates the benefits DVI might have. Opinions are divided on whether DVI is better in practice, as graphics card/monitor manufacturers have become quite good at doing the conversions for VGA.