[wenc]

People often say Mandarin and Cantonese are like Spanish and Portuguese, but that undersells how different they are.

Your example of Spanish and French is more accurate -- same language family, but different grammar and vocabulary.

I offer German and Dutch as another example pair -- same language family as well, but different enough that no one will say "oh they're just different dialects". Dutch is an example of what happens when a Germanic language (Low Franconian) gets it's own state.