For what it's worth, English Wikipedia has a page for "salary" which has been translated into Spanish as "salario." Wikipedia also has a page for "wage," which has not yet been translated into Spanish. The page for "salario" contains all the synonyms user14029 mentioned plus this one: remuneración.
Although the topic of fixed expressions/collocations (such as asesino a sueldo) has been touched on to some degree already, I'll add a bit more here with some examples. What you see below are what appear to be more likely pairings. I'm not suggesting that you can't swap these words out with any of the other synonyms. That's probably just something you'll have to learn as you go and, as has already been mentioned, may depend on the region.
Before I get to the examples, I want to pose a question to anyone reading this, especially native English speakers. What's the difference between "salary" and "wage" in English? If you're not entirely sure, these two StackExchange threads might help:
Wages and Salaries
Wage vs. salary
I realize this is a StackExchange for those who want to learn about Spanish, but sometimes the differences between two words that exist in English are the same ones that exist in Spanish. This thread here is another example.
With that out of the way, let's get to the examples. As you will soon see, it appears that "salario" is the word of choice in many common phrases that can use both "salary" and "wage" in English:
high salary/wage = salario alto
annual salary/wage - salario anual
decent salary/livable wage - salario digno
to negotiate a salary = negociar un salario
hourly wage = salario por hora
This observation that "salario" seems to be more commonly used than "sueldo" is reflective in this Google Ngram chart.
The following show you examples of common phrases that can use both "salario" and "sueldo" even if they might refer to something slightly different:
on a salary = con un salario/sueldo
minimum salary = salario mínimo
minimum wage = sueldo mínimo
And then sometimes you've got to use something slightly different altogether:
wage gap = diferencia salarial
I think this is sometimes translated as "brecha de salario," but in practice, I don't really see much evidence that it is used nearly as often as "diferencia salarial."
And the last one I'll leave you with is this: