What is this WaitForTransform and lookupTransform function overloading do?

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Usually I use method of both tf function that only accept source_frame and target_frame. Recently I discover from amcl source code that there is another function overloading that accepts more argumentd like fixed_frame, source_time, target_time. I have read the documentation and still don't understand what is these function and its argument do.

Even more the code from amcl sets target_frame and source_frame value with same frame that is base_frame_id, why?

  // wait a little for the latest tf to become available
  tf_->waitForTransform(base_frame_id_, msg.header.stamp,
                       base_frame_id_, now,
                       odom_frame_id_, ros::Duration(0.5));
  tf_->lookupTransform(base_frame_id_, msg.header.stamp,
                       base_frame_id_, now,
                       odom_frame_id_, tx_odom);