Is ordering the online version of TurboTax from Amazon as secure as using the CD version? I have always used the CD before, but now my computer doesn't have a CD slot.

Then you would be requesting a download of the TurboTax software to be installed on your personal computer, Not the TurboTax online web-based editions.

The download from Amazon is the same download as provided through TurboTax.

The downloadable installer and the CD installer are the same; as long as you order the installer download from a reputable vendor, it should be the same as ordering it directly from Turbotax.   Your actual tax data will only ever exist on your own computer so it will be as secure as you want to make it.