how wordpress smtp works? my emailing is not working

All of my wordpress emailing is not working. I have created a test file for smtp emailing. it works OK. I put on /test.php and works great! So I think that hosting or server don’t cause this problem.

But on wordpress, all of emails are not working! I use budddypress and contact form 7.

removed all of plugins(23 plugins) except contact form 7. but contact form 7 is not working.

Do I need to setup wordpress emailing to active?
Could it be a Database problem? We moved database to this server(single site) from another server (multi-site). the tables were on 2nd blog for multi-site (you know the table names are like wp_post_2….etc). and changed to the 1st blog (single-site). when we were moving, we changed table names from wp_post_2 to wp_post. it works fine except emailing. I don’t know if you understand what I am talking about changing table names. we moved 2nd blog on multi-site to 1st blog on single-site.
if this problem is with moving database (changing table names), how I check? Do I need to check any tables? which file I should check or test for emailing?