[dba-SQLServer]IP Connection to SQL

To begin, I know next to nothing about network administration, so my
questions may be quite foolish. So be it!

I'm doing some work for a client, working from home on an Access ADP and
hitting the back end (sql 2000) using an IP address, a uid and a pswd. I was
given these three items by the network guy at the client's. I fired up the
ADP, chose /File/Connection and filled in the data -- and that was that!
Total time invested 1 minute, and it works. I can hit the db using EM or
Access. I can create sprocs etc. from either. No muss, no fuss, no Terminal
Services or Citrix, nothing but an IP a uid and a pswd.

What needs to be done to make this happen? I don't don't see a Windows login
or anything when I make the connection -- just the standard SQL login. Does
their router simply listen for hits on that IP and forward them to SQL for
authentication, without doing any Windows-level user checks? Did the network
guy create a Windows user for me and that's how I get in?

The reason I ask is that I have another client that uses TS to connect
remote users to the db, and I no longer see the point in this, given the
ease with which I connected to client 1's db.

Neither client uses integrated security. Both insist on you typing a pswd
before you can hit the db. I want to duplicate client 1's setup on client
2's system. In client 2's case, sql security is all done by means of roles.
I am the only member of the role that has access to the raw data; various
other roles grant increasing access, from read-only on up.

I would love to eliminate TS from client 2's setup and make it just like
client 1's. What steps are required?

Client 2 details: win2k all around, sql2k on the db server; sql logins for
the employees and two other external associates, plus me with admin rights
at both the win and sql level.

TIA,
A.