Why are my mom's contacts on my iPhone? Why are my mom's contacts on my phone, and how do I delete them?

We have different iCloud accounts and different phone numbers and different email addresses.

I need help on how to remove them from my phone without deleting them from her phone
It appears if your device was previously used with you mom's iCloud account, and her contact information was not removed from the device before you signed in with your iCloud account. This will merge the contact data from both accounts. 

Unfortunately, there is no way to automatically detect which contacts were yours or which ones were your mom's.

A simple solution is to manually delete all the contacts that do not belong to you. First, ensure that your phone is using your account for contacts, otherwise you will be deleting your mom's contacts on her iCloud account. Go to Settings > Your Name > iCloud > Contacts and check if Contacts is on and the account is yours. Then, open the contacts app and tap edit on the contact you would like to delete. Finally, scroll to the bottom and press Delete Contact then Delete Contact on the popup again.

If you happen to use Time Machine on a separate macOS device and use iCloud sync, you could try to recover your old contacts list, delete all your contacts, then re-import the original contacts from the Time Machine backup.

To prevent this from happening in the future (as I have done this many times myself on accident), make sure you completely erase your device before signing in with a new iCloud account.