How can I fetch two sets of results in a single MySQL query from the same table?

As the other answer says - you can combine results using union - which simply means to join two results together. What is important to note, however, is that you can't simply union those two queries together directly, as they use order by, so we need to wrap them in outer queries, and use a ranking variable to ensure we can reconstruct the union in the order that we want:

select * from (
    SELECT 1 as tbl, 
           comments.userid, 
           users.username, 
           comments.comment, 
           comments.ratings, 
           comments.datetime, 
           comments.record_num, 
           content.uploader, 
           content.anonymous,
           @rank := @rank + 1 as rank
    FROM comments 
      LEFT JOIN users ON  comments.userid = users.record_num 
      LEFT JOIN content ON comments.content = content.record_num
      CROSS JOIN (select @rank := 0 ) q
    WHERE comments.content = ? ORDER BY comments.ratings DESC limit 3
) q1    
UNION ALL
select * from (    
    SELECT 2 as tbl, 
           comments.userid, 
           users.username, 
           comments.comment, 
           comments.ratings, 
           comments.datetime, 
           comments.record_num, 
           content.uploader, 
           content.anonymous,
           @rank := @rank + 1 as rank
    FROM comments 
      LEFT JOIN users ON  comments.userid = users.record_num 
      LEFT JOIN content ON comments.content = content.record_num
      CROSS JOIN (select @rank := 0 ) q
    WHERE comments.content = ? ORDER BY comments.datetime DESC limit ?, ?
) q2
ORDER BY tbl asc, rank asc;

union by default is distinct meaning that it won't duplicate rows found in both result sets, however there is also no guarantee that the rows will be returned in the order you expect, hence the need to mark each table with its own tbl value, and then order by that field.

If you were certain there would be no duplicates, you could eliminate the duplicate check by using union all, instead of union