I think Verizon has a backup assistant app on most of their phones. So if you're switching phone models, it allows you to backup the contacts from the old phone and restore then onto the new phone.
I believe there are two (at least) sets of contacts that may or may not be backed up. Backup Assistant backs up your "phone contacts". Google Contacts deals with those contacts associated with your Google Contacts.
When you add a new contact, it gives you the option of creating a "phone contact" or a "Google Contact" contact. Something like that.