Why does my Moto Z "Contact" appear different than my online Google Contacts & iPhone Contact?

I'm trying to sync my old iPhone Contacts onto my new Moto Z. I went to Setting/ Accounts/ Google/ my gmail account & I see my contacts were synced 5 mins ago. I switched it off then back on to force the sync again. Then I go to my gmail account on my laptop & open Contacts. The Contacts in there seem to be right & match up with what I see in my old iPhone Contact. But when I click on the Contact App on my Moto Z it doesn't match either of the other "Contacts" lists. More irritating it has...

Why does my Moto Z "Contact" appear different than my online Google Contacts & iPhone Contact?

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