These methods use the read method to accomplish the actual read. The method which takes the LSN of the current record reads the log record at that LSN and supplies it to the other read_next_logrec. This method uses the length of the log record to compute the LSN of the next log record and reads that in.
It is obvious that it would be more efficient to call the second method if the current log record is available rather than getting its LSN and calling the first method.