it means what a reasonable person would see as equivalent
Unless the contract provides some other mechanism. For example, if it says “at the principal’s discretion” it means what a reasonable principal would consider equivalent, which might be different from a reasonable person. If is says “at the principal’s sole discretion” it means what this principal, acting reasonably, finds equivalent.
As a bare minimum it must be functionally equivalent. That is, it must serve the same purpose. An umbrella is not functionally equivalent to an M10 bolt but an M12 bolt might be.
It might need to be technically equivalent (or superior). An M10 bolt is not technically equivalent to an M10 bolt with a lower tensile strength. Similarly, a mild steel galvanised bolt is not technically equivalent to a stainless steel bolt. Even if they were functionally equivalent a reasonable person might accept or reject them. As such either decision by a principal would be a valid use of their discretion.
It might need to be aesthetically equivalent. This is generally more true of items like cars, toilets, door hardware etc. than it is of bolts but it can even apply to bolts if they are on display.
Prior to a contract, a supplier would have no cause of action against a purchaser who unjustly rejected an alternative although, for a government agency, they may have cause for complaint.
During the execution of a contract, rejection of an alternative could be disputed just like any other use of discretion.
