Screw terminal are the most expensive and probably the strongest device for mechanical reason at the terminals. They are frequently held in place with clamps.
The leaded terminal caps might not get large enough (high capacitance and voltage) to meet the needs, leaving the snap-in caps the choice for many mid-sized caps. Might not be the same as what came out but can usually be made to work.
Obviously, it is easiest to replace screw terminal with same especially if the lead spacing in the same, almost drop in but the hole in the wiring bracket might not be big enough for a larger screw (a short bolt, actually) sometimes used on newer caps. A simple drill out of that hole and with the same diameter cap the clamp will fit. Otherwise, folks use all manner of kludges to make the clamp tight on the cap, including using a smaller clamp since most caps are smaller today for the same specs.
On the snap-in, they many times replace a leaded cap and might fit just fine if the lead spacing is the same. If not, work is done to make the electrical connection and as Steven stated above to allow the dummy leads to be attached without any electrical connection, just mechanical. This is another way the recapper gets to use his abilities to get the cap in correctly and firmly mounted without compromising the electrical system.
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