Email Not Sending

I was using the "via PHP mail function" when I had my store on a test domain and it was working perfectly. Since moving to the live domain, I have noticed that no emails are sent and no emails are received through the 'contact us' form. It is the exact same store (v4.6.2). I have tried using the SMTP function but I get this message:

Error Message could not be sent.
Mailer Error: SMTP connect() failed.

If I use PHP, it says the email was successfully sent but it never is received, can anyone advise, please?

Many thanks

Suggest you contact your hosting provider. I would guess it is a server config or ssl issue on your site. Note that php mail function will be seen as spam by many mail providers.