The connector moves the sear down, out of engagement with the striker, after the sear has pulled it back. Different connectors have different angles, which is why you can drop them in and change trigger pulls. They drop the sear down earlier or later in the trigger pull. Some brands of aftermarket connectors have a trigger stop, an extra projection on the connector that an armorer can file away until there is just enough room for the sesr plate to fall before rearward movement of the trigger stops.
There really isn't a similarity to your 1911s or CZs. Different system.
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