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The status and definition of the Roman colonia varied greatly depending upon the timeframe involved. The simplest definitions were during the time of the Roman Republic. The two major forms of colony from 500 BC to 133 BC were the Roman Colony, and the Latin Colony.
Information on these basic colony definitions can be read
But that's were the simple explanations end. The city you are discussing, Carteia, really is a transition point, and is literally the first colony of its kind. Up to this point the Roman colonies were pretty close to home. Carteia, located near the Straits of Gibraltar, in the then Roman territory of Hispania, was a garrisoned city that had existed since 940 BC. It had been captured by the Romans in 190 BC.
Livy is the source for the information concerning the petition for status within the senate, which, in 171 BC granted the status of 'Latin Colony' to the captured city of Carteia. This was the first colony with this designation outside the Italian Peninsula. It granted its citizens more rights then they had, but not the rights of full Roman citizens.As a Latin colony they received right to marry, and the right to conduct business. The Colonia Libertinorum Carteia (Freedmen's Colony of Carteia) may have been unique in its status.
At this point, typical politics took over, and numerous other locations gained colony status, but often mainly as attempts to curry political favor among one group or another, so the clearcut definitions from above become harder to apply. As mentioned in the article on Latin rights,
The acquisition of ius Latii was wholly dependent on imperial gift.This beneficence could span the whole range from grants to individuals to awards made to whole towns, and could even be applied to an entire population, as when Emperor Vespasian gave the ius Latii to all of Hispania in AD 74.
I have to admit the 'freedman' designation apparently given to citizens in Carteia, as it seems different then that of Latin Colony. As mentioned in the wikipedia entry for freedman, freedmen were granted the right to vote, which members of a Latin colony were not. Possible some Roman legalese to infer rights 'after the fact'? Still looking for more on this...
I hope this helps clear up some of the confusion, basically up until the Carteia colony there were pretty simple rules, with two types of colonies. After 133 BC, it became politically defined and assigned at the whim of the Senate.