Thanks for sending through the two example emails.
I think I've found the significant difference between the two.
From Tectite FormMail:
So, in the first case, GMail can see that you're sending email to yourself.
In the second case, it's someone else's address that's sending to you. That combined with the fact it's about "escorts", probably makes it spam.
To get the same header effect with Tectite FormMail, you need:
$FIXED_SENDER = "YourAddress@gmail.com"