If you are hosting at Ionos they have disabled the mail() function so you will have to use the PHPMailer option. Instructions for SMTP PHPMailer on this page. You also have to be using Sytist 4.8.2 or higher.
When an email is sent from Sytist, Sytist calls the function to send the email and then it is up to the server to deliver the email.
AGAIN: Sytist calls the function to send the email and then it is up to the server to deliver the email.
Go to Stats -> Email Logs and you will see whether or not Sytist has sent the email. If you see the email sent then then Sytist did it's part so the issue is on the server side.
Gallery invite emails are not sending but order emails and others are?
This can happen if you have enable Automated Emails but the cron job on the server to make it work is not set up correctly or not working. You can go to Settings -> Automated Emails and it will show if there are pending emails. If so then this is the issue. You will either need to disable automated emails or set up the cron job on the server correctly.
Going into Spam folders
If they are going into spam you can get with your host about enabling SPF and DKIM and check to see of the IP address of your website has been reported for spam. Most of the time there are many many websites using the same IP address so if one get reported it will affect the other accounts.
Some things that may cause all emails not to be received
* You can send test emails in Settings -> Mail Sending Settings.
1) Settings -> Admin / Main Settings -> "Name of your website".
This is the from "name" when emails are sent. Do not enter a web address. Example, do not enter www.picturespro.com or http://www.picturespro.com or picturespro.com. Enter the name of your business like Joe Bob Photography - Destin Florida.
Having an URL in that section can cause emails to get rejected by the server.
2) Settings -> Admin / Main Settings -> "Contact Email Address"
This is the default email address emails are sent from. It is possible your hosting company requires that you use an email address @your-domain (example: info@picturespro.com ). If you are using something different (like a yahoo or hotmail email address), try using one @yourdomain. You can set those up in your hosting control panel or contact your hosting company for assistance.
NOTE a @yahoo.com email address WILL NOT WORK. Yahoo won't allow emails like that to be sent from the server now in most cases.
Use SMTP PHPMailer If You Are Still Having Issues
In Settings -> Mail Sending Settings there is an option for the standard mail() function which is the default option.
There is also a PHPMailer option which uses the actual mail servers to send the emails and has a better chance of getting into inboxes.
Instructions here for setting up PHPMailer.
IF NONE OF THE ABOVE WORK YOU WILL HAVE TO GET WITH YOUR HOSTING SUPPORT BECAUSE THIS ISSUE IS WITH THE SERVER. NOT A SYTIST ISSUE.