When economists think about skills, we really just mean the bunch of job-specific expertise and transferable attributes that make a person well-suited or not for a job. Defined as such, nobody can deny skills’ importance in determining wages.
If you have higher abilities at football or coding, you will likely make a greater contribution to your club or company’s profitability, giving you leverage when negotiating for higher pay. If you acquire talents for a job through experience or study, you become less easily replaceable by others. Those skill-dependent demand and supply factors tend to make you higher paid, holding all else constant.
Yes, there are certainly other important wage determinants. Footballers get paid more than, say, ice hockey players because there is a bigger viewing market for their talents here. Demand levels for products and profitability conditions for businesses are crucial for determining labour demand, while demographics, job prestige and the state of the economy influence the supply of workers for a particular role, affecting pay rates too.
The key point though is that, in economics, “skills” that contribute to wage rates are contextual to the role. Tiger Woods is skilled at golf, but would probably make a fairly useless plumber. I have a masters degree, but if I time-travelled back to an Elizabethan shipyard, I’d be very low-skilled for the employment on offer.
It therefore makes little sense to describe someone as a “low-skilled worker” as if that denotes an aggregate measure of one’s capabilities. Different jobs entail different skills, which are often both hard-learned and incomparable by metric. It’s overwhelmingly within a particular job market that skill affects your labour productivity and so your wage.
Unfortunately, the term “low-skilled worker” has different connotations in politics, where it is generally used as synonymous with either a person having a low level of formal education or being paid a low wage.
Such conflations are problematic. Trades that might require low levels of formal education are often deemed “low skilled”, even when they require extensive experience or on-the-job nous. That elitism is unhelpful in a society that desires equal dignity, especially for roles that are essential to society functioning, such as care or maintenance industries.
More pertinently for these trade negotiations, “skill” in immigration law gets proxied for by the wage rate for a formal job offer open to the desired migrant. A immigrant worker’s pay offer today is deemed the best signal for whether someone has the desirable skills to actually work here.