typically, Normalizing does the exact same thing as adding gain, but doesn't allow any peaks to go over 0dB. Normalizing will find the highest peak in the file, and make that 0dB (or -.5dB, or whatever you set it to), and will raise the gain of the entire file by the same amount. This should sound the same as if you did the process yourself (by determining the what the highest peak it, and then adding gain manually to the whole file).
The confusion comes in here. In some software programs (I'm at work, so I don't have WaveLab open in front of me), there is an option to Normalize based on average RMS value. What that does is it'll raise the average RMS value of the whole file to a specific point. The problem with this is that it doesn't look at the peak values at all, so if you raise the average RMS level by too much, it could push the peaks beyond 0dBfs and create clipping. You don't want to normalize with this method. But if you stick to the first method (Normalize based on peak values), you'll be all set.