Can two emails with different IP addresses come from the same person /
systems. Such as: 172.18.180.134 and 172.18.150.229 ?

Yes. IP addresses can be changed easily by requesting a change from
ISP. Dial-up users need only to reconnect to get a new IP address.

Depending on the type of the internet connection and time, yes it can.

If the person is using a dial up connection everytime s/he connects
the DHCP server will assign a new IP address.

If the person is using a nailed connection (cable,dsl etc.)if the time
between mails are so close there may be a reason for being suspicous

Judging by those example IP addresses, those are private class 2 IP
addresses, and not public IP's.  This could be someone being logged
into two different computers sending email on a corporate network that
is subnetted into different networks, like different locations, etc.

IT employees typically remote into other PC's, and sometimes send
emails from those machines in which they are remoted into.

Hope I'm not too far off here.  ;)

Steve