Workman's Compensation Insurance is specifically for work related injuries. State laws control the way WCI is regulated, meaning the requirements that are needed to collect a claim, the amount of the claim and so forth. Not all employer's are required to participate in WCI therefore not all employee's would have access to the program.
In the UK an employer is responsible for injuries caused in the workplace if the employer was in some way negligent or breached other UK regulations. For example - if a workman hurt his foot due to a defective work machine - the employer would be liable to pay compensation.