Hey there, Rick!
Thanks for visiting the Apple Support Communities. I understand you'd like to know if dialing emergency services from your Phone app will also alert emergency contacts, like using the Emergency SOS feature would. I'm happy to help!
According to the information in Make emergency calls on iPhone - Apple Support:
"In case of emergency, use iPhone to quickly call for help. With Emergency SOS, you can quickly and easily call for help and alert your emergency contacts."
This indicates that dialing from the Phone app will not alert your emergency contacts, while using Emergency SOS will.
If you do need to use the Emergency SOS feature but do not want your emergency contacts alerted, you can choose to cancel: Use Emergency SOS on your iPhone - Apple Support.
Have a good day.