Can I transfer messages from iPad to iPhone without using Icloud

If you were to restore the iPhone from a backup of the iPad, they would appear on the iPhone, yes. If you are saying that you are trying to get messages from the iPad that you deleted from the iPhone over, no, that is not possible. You cannot selectively restore bits and pieces of a backup.

If you received the messages in your email instead of messages, you can save that. However neither way can you get the message from the iPad to the iPhone, except as described above.