To identify the emails came from the same IP address, check the headers. There may also be clues, depending on mail program, that show similarities between the sender's machine. It is possible for two emails to originate from different IP addresses and yet the same computer, but highly unlikely that two emails with the same originating IP would be coming from different computers (unless it came from a network sharing a connection). If IPs are different, but in the same leased range (do a whois using samspade.org), it could still be the same computer, just an expired IP lease. It is typical every 5-7 days for a SP to renew IP assignments to customer connections.
The whois lookup will let you know if both IPs (if they are different) are leased by the same SP.