They were fairly common in organizations with more than one location. As mentioned, years ago 7c message units could add up to some serious money so even a local tie line between plants within a city was cost justified. (Our hospital had five tie-line trunks to the independent rehab center next door.)
Also, many PBXs of the old day limited extensions to in-house dialing only, no outside calls to save money. But tie-lines weren't charge so they were allowable and allowed employees to conduct business.
Tie lines usually allowed direct dialing in a PBX at another location. You dialed a special code (often 8 or 8+) and either merely immediately dialed the distant extension or waited for a second dial-tone, then dialed the extension. For larger organizations, the tie-line access codes could be quite large. For Centrex users, tie lines had their own 3 digit code different than the outside code to allow direct inward dialing.
Some tie-lines were relayed from PBX to PBX, you kept dialing the access code and tied together a bunch of systems. I don't think that was the preferred way, however.
Tie-lines usually allowed dialing in both directions between the two PBXs. I know one switchboard could connect an outside caller through the tie-line to the remote location, but they didn't like to do so as a matter of policy. The tie-line jacks on the switchboard were a little more complicated -- there was a pair for each line, one jack used for answering, one used for calling.
Other remote locations may have been served by a simpler extension basis. That is, the home PBX could only reach the remote PBX operator who would have to complete the call to the desired remote extension. I presume this wiring was far simpler than tie-lines due to one-way instead of two-way signalling.
Yes. My employer once had a network of tie lines to our various locations and associated codes for them -- each location having its own code. Our centrex phone numbercards had two lines -- one our regular number, one our tie-line number. Some years ago all that was eliminated. To reach a distant location outside our local PBX or Centrex, we just dial 9+ the external number. The equipment switches it the most economical way available when the call is made. (My employer has a series of LD methods from outward WATS lines down to regular toll network, maybe some tie-lines or FX lines remain but they are hidden to us.)
Probably the biggest network is the Federal Govt's "FTS" network and the military's Autovon network. I don't know how they work today. I always thought "Autovon" used special TouchTone phones, but at my father's installation, the Autovon lines came in the PBX just like any other trunk and the phones in his place were plain rotary. They used Autovon for plain business, not "combat" situations as the literature suggests. FWIW, they converted to Centrex from PBX, then closed the whole place down about six months later. It appeared the govt owned, not leased, the PBX switchboard and switchgear--with govt employees doing the maintenance on it, not Bell people, even though it was connected to the Bell System.
Of course on the other hand, Centrex is now available to very small businesses with wide locations using regular numbers. (Originally you got a dedicated or near dedicated NNX all to yourself and a huge block of numbers. For some reason, many, though not all, of the oldest Centrex's of the 1960s have received new exchanges; I don't know why.)
[TELECOM Digest Editor's Note: And don't forget the other close relative in that cluster of service types: the OPX or 'off-premise- extension'. When I worked (back in the late 1950's/early 1960's) at University of Chicago in the phone room, there were a bunch of these that were located all over the Hyde Park neighborhood. You'd see phone booths around the area with both a payphone in them _and_ a University of Chicago OPX. Almost all the dormitories had their own switchboards with outside phone numbers, but two or three OPX numbers terminated on those switchboards as well. Those OPXs were all of the four digit extension type number, and I guess when the most recent form of Centrex was installed a few years ago, all those OPXs took the new number 753-xxxx. PAT]