I do think there's more class granularity than that, and it's important to understand how such distinctions can make it more or less difficult to organize and cooperate. E.g. the idea of a petit bourgeoisie is useful for understanding why small business owners, despite indeed needing to work for a living, are generally against unionization.

But the core of your point certainly stands. "Higher wage" vs "lower wage" does not make a big difference in terms of our fundamental interests, and the interests of workers are far more similar than people realize.