there is also a doc link where log configuration is described:
You can modify log configuration in conf directory according to logging framework docs.
.log and .out are different. Usually, the .log file stores the log information output by the log framework. Flink uses slf4j as the log interface and supports log4j and logback configurations. The .out file stores the STDOUT information. This information is usually output by you calling some APIs such as the print sink API.