What is the difference between three methods of a log file creating, which are offered by plugin?

All methods are equivalent, so when you turn on them all only one of them will work.
There may be unwanted conflicts.

1) Error logging via '.htaccess' using 'ini_set'

This method is suitable if you have an access to the file ".htaccess" to edit it.
Also, this method allows you to create a log file, its name, change the absolute path to it.
'php_flag' and 'php_value' change the value of Apache directives by changing the server configuration. The plugin uses this method only to enable PHP errors logging and specifying the path to the log files. Other configuration settings you can change by yourself.

For more information, please visit How to change configuration settings and Directives list php.ini

2) Error logging via 'wp-config.php' using 'ini_set'

If you don't have an access to ".htaccess", you can use file "wp-config.php" to change server configuration settings using the 'ini_set' option and specifying a variety of error logging settings and other options. The plugin uses this method only to activate the PHP error logging and specifying the path to the log files.

For more information, please visit Runtime Configuration and ini_set

3) Error logging via 'wp-config.php' using 'WP_DEBUG'

This method is used for debugging errors using the WordPress PHP constants and declaring them in the "wp-config.php" file. This is a standard WordPress debugging method. This is a very good method which is recommended for using on WordPress sites, but errors are recorded in the file "debug.log" to the 'wp-content' directory. You can’t change the absolute path to file logs. This method is considered to be a priority on the WordPress sites. After declaring of these constants other methods won’t work.

For more information, please visit Errors Debugging on the WordPress


This article related to Error Log Viewer plugin

Additional resources: Error Log Viewer - User Guide

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