The ESET Online Scanner looks at your system from a different perspective than a typical ESET Computer scan.
Generally speaking, there's no need to make use of the ESET Online Scanner if the computer is already running an ESET program. This web-based scanner is really more for folks who use a non-ESET product and want a second opinion (or no anti-malware software and want a first opinion).
The ESET Online Scanner's modules and virus signature database are updated concomitantly with those for ESET's other products, so any difference in detection could simply be due to differences in configuration or in update intervals on the client side.
Actually, if you suspect something got past your ESET Antivirus, there is a good reason to boot into safe-mode with Networking and run an online scan- as mentioned, the software runs differently from the resident ESET - and I have had ESET online find a threat that the regular did not (only once).
If you do not suspect your machine has a problem, then I wouldn't bother running it - and if I did run online scanner, I wouldn't bother UNLESS I was in safe-mode w/networking.
Regards,