Does each country which uses Spanish as a mother tongue have its own accent or its own expression like English? Like Mexican accent, Argentina accent, etc...

Yes, every country sounds different. But the main differences between Spain and Latin America are those:

▪In Spain we differentiate between letters "c/z" and "s", but in Latin America they don't. What Latin Americans do is called "seseo".

Spain:

C/Z - θ sound (th in English)
S - S sound

Latin America:

C/Z/S - S sound

▪In Spain we use the pronoun "vosotros" in informal situations and "ustedes" in formal ones. But in Latin America they always use "ustedes" (so when they come here they always seem very formal).

Spain:

You = Vosotros/as (informal)
You = Ustedes (formal)

Latin America:

You = Ustedes (formal&informal)

▪In Spain we have a neutral tone, our entonation is plain. In Latin America they sound as if they were singing, in some countries more than in others.

▪And there are many different words and expressions that we use, of course.

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Those are the differences in general, but inside Spain and inside Latin America there are many more differences and different accents. For example, in the Canary Islands (Spain) they sound more similar to Latin Americans than to peninsular Spaniards. They have seseo and they always just use "ustedes", too. Also, in the south of Spain some people do seseo, but not always. And in the south it also exists the ceceo, which is the opposite, to pronounce "s" like "c/z", but it's very uncommon. Usually people in the south of Spain just differentiate the sounds or make a mix between differentiating, seseo and/or ceceo. And in Argentina, Uruguay and Paraguay they don't use the pronoun "tú", they use "vos", and they also make a different sound for "ll/y", like a "sh" sound. And lastly, many people don't pronounce every letter while talking, I mean, they don't say the "s" at the end of the words and some letters more. But that's not a difference between Spain and Latin America. That happens in many different places: the south of Spain, the Canary Islands, Argentina, Uruguay, Chile, Puerto Rico, Cuba, Dominican Republic, etc.

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Here you have some videos for you to compare:

▪Spain

- https://youtu.be/GgbOx_L7rQ0 (neutral accent)
- https://youtu.be/rxcBQNCl3B8 (neutral accent)
- https://youtu.be/LfYN9iL1aA4 (south of Spain)
- https://youtu.be/6dpx1JjjjXI (south of Spain)
- https://youtu.be/NDMZEDvnrxI (Canary Islands)

▪Latin America:

- https://youtu.be/ZCIhJqQxyqA (Mexico)
- https://youtu.be/oemR9oZAJfE (Colombia)
- https://youtu.be/e7Hh7WtgaFk (Argentina)
- https://youtu.be/J5YprICLV_I (Venezuela)