You haven't said if you are using iCloud Photos to sync Photos Libraries on your devices.
If you are, then iCloud Photos will copy all Library pictures from a device to iCloud Photos and then copy those to all other devices. iCloud Photos will ensure that the pictures on all your devices are exactly the same. That means that if you delete a picture on you iPhone, then the same pictures will be deleted everywhere. Of course, they can still be seen in Recently Deleted, and they can be restored for 30 days.
If you turn on iCloud on your Mac, then any pictures that aren't already in iCloud will be copied to iCloud Photos, and then they will be copied to all other connected devices. And any pictures in iCloud Photos that aren't on the Mac will be copied to its Photos Library.
Keep in mind: if you delete pictures from the Recently Deleted view, they will be permanently deleted everywhere-- in general that's a bad idea. Having 30 days tho change your mind is a gift!