All Exceptions that happen on the Magento site comes in Exception.log. Ultimately an exception happens when Magento is not able to detect the correct data to load a page or a feature. When this error happens Magento logs that in exception.log.
All Php warnings, XML-file errors, and other warnings comes into System.log
The var/log folder in the site directory contains the log files along with error logs for your Magento 3rd party modules (extensions, etc). The Magento system log file (system.log) and an exception log file (exception.log) are saved to the var/log folder unless you rename it from the admin panel in the system>configuration with different file names.
It’s important to know what these locations are, so you can easily debug the errors. Again, exceptions are for correct data and XML, and the system is more for PHP warnings and errors for advanced processes on the site.
If you look for these files or folder and don't see it, then there is a chance that the log is disabled in the Admin panel. In Magento you need to the log on; You need to go to Admin -> Configuration -> Advanced -> Developer -> Log setting.
It will not bring in old information but rather start logging information from that time forward. Be careful if you plan on leaving this logging process on. I've seen many sites that have been bloated by the log files, especially by sites with high traffic loads. If you aren't using the log to resolve an issue I recommend turning it off.