iphone and mac aol mail does not update.

Is the account using IMAP or POP? With IMAP then this should reflect mail on each device.

Have you turned on 2 factor authentication & authorised the account or created an app specific password for AOL? They changed their email security a while ago & people have been having problems since.

These don't sync between devices Contacts, Calendars, Bookmarks, Notes, Voice Memos, shared photos, iCloud Photos, and emails. Each device syncs to the email account server which may be Google, iCloud, AOL, Exchange, Outlook, Yahoo, or any Other. Please see the pic below

If one of the devices is not connected to the internet then it may seem to you that they are not syncing.