A tie-line is a full-time private connection, accessed either by inserting a TRK cord into a tie-line jack (in the case of a manual PBX) or by dialing an access code (in the case of a dial PBX) or by selecting a key on a key set (in the case of a key system). It signals an equivalent unit at the distant end, which is assumed to be at another premises. The answer to your question is that you need a 415 at "this" end and one at "that" end. The cards are plugged into two separate KSU's, one at each of the premises that are tied together over a distance of several to many miles.
Key system-based tie-lines can be automatic, or manual. The 461A KTU is a manual unit. The 415 is an automatic one. The circuits at both ends need to be electrically equivalent, in most cases. There are situations where one end would be automatic (immediate ring-down upon going off-hook) and manual ring-down at the other end, but those cases were extremely rare.
"(I) can't help wonder, if there are 35+ line cards, but a 551C can only use 4 of them?"
Because the 35+ types are used for 35+ different jobs. It would be highly unlikely that any installation would require one (or more) of every type of KTU. Generally, they would be mostly CO line cards, with a few manual intercom (401) cards. It was a rare occasion to find a tie-line card, because the mileage charges between subscribers was prohibitive. They were installed for customers who "did the math" and figured out that the toll charges for dial-up calls between their premises were more than the cost of a private, non-dialed, connection.
In later years, ISTR in the 1980's, the BOC's offered an automatic ringdown circuit that was based entirely on central office equipment, with just a T&R appearance at each end. I don't remember the exact USOC, but I will do a little research and let you know.
