Differentiating computers on same network

What would I be looking at to differentiate computers on the same
network? (using Ruby/Rails code) Also considering computers that are
assigned a different ip over a wireless office network. Would I be
looking at extracting the MAC address or is there a better way?

Unsure what you're trying to do here, but you perhaps want to be
looking at using session or cookie information to identify unique
users of a rails app.

If however, you are asking a more generic networking question...then
IP's are non-unique. Take for example multiple computers (CPE's)
behind a NAT-router. They will all appear as the same IP on the WAN
MAC addresses are unique. However, they can be spoofed/modified and as
such are not a secure way to identify 'unique-ness' either. Take the
same example of the CPE's behind a NAT-router. They will all appear to
the WAN side as a single MAC address for their network traffic. (This
is in-fact how Internet routing works).

So basically MAC addresses will not transit a router in the network as
they are Layer 2 entities. IP's are Layer 3+ and will transit routers,
but not NAT routers (which are very common).
I'm sure it is possible to get MAC information via a cookie or some
such inquiry, but that is no guarantee of uniqueness considering that
MAC's can be modified.