True, and Mandarin would be the better word to use here. Mandarin and Cantonese are for all intents and purposes separate languages. They are more different than English and Spanish.
Chinese is the written language, based on Mandarin. Mandarin and Cantonese are separate, though closely related, spoken languages. They're a lot closer to each other than English and Spanish (more like French and Spanish), which is why the same written language works for both sets of speakers: most of the vocabulary is shared.
This is only because almost all native Cantonese speakers are trained to read and write in Standard Chinese from the very beginning.
Standard Chinese can be spoken in Cantonese, but while understandable, it is never done, in contrast to Mandarin.
In recent years written online conversations (like blogs, Facebook posts, instant messages) by Cantonese speakers are increasingly written in Cantonese instead, and this is slowly spreading to more "formal" media such as books.
Yes, it seems I underestimated the difference: "In spoken Cantonese the frequency of use of Cantonese dialect words is
close to 50 percent (Li, et. al., 1995, p236)." (from https://www.aclweb.org/anthology/P98-2238.pdf).
If we're going down that path, then it should more specifically be Standard Mandarin, since Standard Mandarin and e.g. Southwestern Mandarin are only partially mutually intelligible like French and Spanish are partially mutually intelligible.
