Who knows what the difference is? Besides being designed by different designers.
Cheers
“The new typeface’s refinements included special rethinking of details such as the letters’ terminals and stroke endings, as well as the fonts’ spacing and the kerning.” (http://www.linotype.com/5737/tradegothicnext.html)
“Many additional features were added into the typeface during the design process. Each font includes small caps and oldstyle figures. There are also a number of alternates”. (http://www.linotype.com/5798/dinnext.html)
Do you think it makes any difference in webfont rendering?
That would mainly regard hinting, so you will need to compare directly the output of the various offerings.
For example: http://webfonts.fonts.com/en-US/Project/ChooseFonts?fontQuery=din
“Next” is simply Linotype’s label for typefaces that they feel have been revised enough to warrant a new name. Some are more comprehensive revisions than others. Of course, marketing does have something to do with this, but the distinction is also useful because the typefaces really are different.
The Next label has no direct relation to webfont quality. As Riccardo said, the best way to judge that is by viewing screenshots. Webfonts.fonts.com offers the two Trade Gothics and DIN Next. DIN (the original name is indeed all caps) is also available as FF DIN Web (no screenshots yet available, but I can tell you it's quite good) and PF Din (screenshots), which is quite a different design.
Captured from web.archive.org on 23 Jul 2019. view this capture