Is "Mexican" a language?

My neighbors' parents were born in the country of Mexico and both speak English and Spanish fluently. Anyhow, today at work someone said, "He speaks Mexican good (sic)." and I corrected him by saying, "Mexican is not a language. Do you mean Spanish?". He said, "No. There's a... show more My neighbors' parents were born in the country of Mexico and both speak English and Spanish fluently.

Anyhow, today at work someone said, "He speaks Mexican good (sic)." and I corrected him by saying, "Mexican is not a language. Do you mean Spanish?". He said, "No. There's a difference between Mexican and Spanish."

So, when I saw my neighbors I asked them. They told me there was a difference but couldn't explain what the difference was.

My thought is that American and Australians have venacular common to their culture, but we don't say that we speak American. We speak English.

So, I'm lost. Is Mexican a language and, if so, what's the difference between Mexican and Spanish?
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