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In some languages, there are different spelling standards in different major dialects. For example:

• 
  British English / American English
  
  
  • colour, aluminium / color, aluminum
  
  


• 
  Catalan / Valencian
  
  
  • cinqué, arrencar / cinquè, arrancar
  
  


• 
  European Portuguese / Brazilian Portuguese
  
  
  • anónimo, óptimo / anônimo, ótimo
  
  

Are there similar examples of spelling differences in different Spanish dialects? Or is it completely standardised?

Some may say that there are not, however there are two special cases where there are spelling differences:

• 
  Vídeo (Spain) | Video (Latin America). This one is due to the differences in pronunciation. Spaniards tend to stress the first syllable (VÍ-DE-O), while Latin Americans stress the second syllable (VI-DÉ-O). Both spellings are recognized by the RAE.
  
  
  • As ukemi points out, some other differences derived from different pronunciation are: buganvilla / buganvilia; béisbol/beisbol; vomitar/gomitar; hierba/yerba; jericalla/jericaya
  
  


• 
  Méjico (Spain and Latin America) | México (Mexico). Now, the RAE recommends the use of x in words like México, and mexicano. However, not so long ago, the use of j was pretty standard everywhere but in Mexico when spelling those words (and, as I understad, still common in some regions of Spain).
  
  
  • Similar to the last one, in Mexico there are a lot of toponyms where the use of x and j still varies from place to place. Oaxaca/Oajaca; Texas/Tejas; Jalapa/Xalapa; Xalcomulco/Jalcomulco; Xilotepec/Jilotepec.
  
  
  • Back in 1815, the RAE stated that all /j/ sounds must be written with a j instead of an x. For example: Quixote -> Quijote. However, in Mexico (back then, in the middle of the Independence War) this rule was never fully applied. This is why there's that particular spelling drift.
  
  

I know that it's not your exact question, but please consider that the dialectic drift in Spanish is heavily marked in other features of the language (like semantics, use of pronouns, verb conjugation, pronunciation, use of foreign words), and not so much in spelling.

Bello orthography

From 1844 to 1927, the government of Chile, (and some other South American countries influenced by this) followed and recommended an adaptation of Andrés Bello's revised Spanish orthography:

1. Substituting ⟨j⟩ for "weak" ⟨g⟩ sounds (jeneral, jinebra)


2. Substituting ⟨i⟩ for ⟨y⟩ used as vowels (rei, i);


3. Writing ⟨s⟩ instead of ⟨x⟩ before consonants (testo).

However, the original spellings eventually regained popularity and Chile returned to following the RAE's orthography after this date.

Individual examples

As prm296 says there are a number of Mexican toponyms etc which use the historical "x" in place of "j"; and words which are pronounced differently in Latin America vs Spain and whose orthographies reflect this (e.g. béisbol/beisbol etc, as well as a number with orthographies not recognised by the RAE e.g. cónyuge/cónyugue).

There is also the occasional word in seseo or yeísmo regions that has taken on a homophonic alternative spelling:

• membresía / membrecía (Mexico, Colombia, Peru)


• jericalla / jericaya (Mexico)

As well as replacing hi → y, hu → gü, b/v → g, ñ → ni, ll → li:

• hierra / yerra (Argentina, Bolivia, Uruguay)


• huero / güero (Mexico)


• buey / güey (Paraguay)


• vomitar / gomitar (Costa Rica, Perú, Bolivia, México, Puerto Rico, El Salvador, Colombia, Chile (rural))


• pergeño / pergenio (Nicaragua, Chile, Uruguay)


• buganvilla / buganvilia (México, Guatemala, Honduras)

Apart from a few words (see other posters) the spelling is identical, whereever you are. In general, you won't be able to determine the origin of a speaker by his spelling - but by the choice of words.

I think that Argentina is the only place, where you intentionally spell differently. There I could see plenty of billboards with a spelling that would be considered incorrect anywhere else. Apparently, in Argentina the root of a verb doesn't change in the imperative or other forms as it would elsewhere, e.g., "probalo" instead of "pruebalo".