Does ward count as a triggered ability or a replacement effect?

Ward is a keyword ability that functions as a triggered ability, not a replacement effect. According to CR 702.20, ward causes a triggered ability to go on the stack whenever the permanent with ward becomes the target of a spell or ability an opponent controls. That trigger reads: "Whenever [this permanent] becomes the target of a spell or ability an opponent controls, counter it unless that player pays [cost]."

Because ward is a triggered ability (CR 603.1), it uses the "whenever" trigger condition and goes on the stack like any other triggered ability. This means it can be responded to, and there is a window between the trigger being placed on the stack and its resolution. Replacement effects, by contrast, modify events as they happen and never use the stack (CR 614.1).

An important consequence of ward being a triggered ability is that the original spell or ability targeting the warded permanent is already on the stack when ward triggers. The opponent must pay the ward cost (or have it countered) upon the ward trigger's resolution, not at the time of targeting.

Example: Your opponent casts Lightning Bolt targeting your Ledger Shredder (which has Ward 2). Ward triggers and goes on the stack on top of Lightning Bolt. Your opponent must pay 2 when the ward trigger resolves, or Lightning Bolt is countered. If they respond to the ward trigger by casting something else, the ward trigger is still waiting on the stack.

Because ward uses the stack and can be responded to, it is definitively a triggered ability under CR 702.20 and CR 603.1, not a replacement effect under CR 614.