In a data step you can write output to file or another output destination. The PUT will write to any of the open destinations but putlog only writes to the log.
A brief example program.
data _null_;
file print;
put 'This will go to the default output destination';
putlog 'This should only appear in the log';
run;
Copy the above code into your SAS session and run it. You will likely not find "This will go the default output destination" in the log but it should be in the Results or Listing output window depending on how you are running your session. The Putlog statement will.
Many years ago, and still do occasionally, use Put statements to write text to specific types of file formats such as text that needs to start in specific columns or lines on a logical page.