The router on the OP's network was probably just being a router. No fancy NAT junk, and probably no ACLs / fireballing. It was pretty common to have something like a T1 circuit, a CSU/DSU that connected to the T1 and presented a serial connection, and a PPP or SDLC connection to your upstream ISP over that serial connection. The router's Ethernet interface is connected to your switch (or hub) and all the hosts have IP addresses in the subnet your ISP assigned. Fancier shops might have a proxy server or dedicated firewall box between the LAN and the router.
Back in the 90s your ISP would have given you a subnet of public IPs to use. I have a Customer w/ a T1 that they've had since the late 90s with the same /26 of public addresses on it the whole time.
The office ethernet network just contained a router, which would be hooked up to the upstream (via multiple T1 lines, IIRC). So everything on the office network had a public IP and was directly on the internet.