I've always wanted to be able to distinguish tarantas, mineras, and cartegeneras. After listening to a bunch of them, I continue about as confused as ever. There are a few things I noticed, however.

Bob Clifton, on the flamenco discussion list, points out that there is a 'jump' in the melody in mineras cante. I noticed this, for example, in the minera sung by Camarón (on the 'Son tus ojos dos extrellas' record). This is the one where Paco de Lucía accompanies in G#, which, according to Paco Sevilla, was innovative for cante accompaniment (Ramón Montoya had a solo in that key, but everyone accompanied cante in the F# tarantas key).

I always assumed that the melody that Camarón sings there is the minera melody - Montoya plays a falseta with essentially the same tune. However, I've heard people sing this same melody por tarantos, particularly for dance. For example, Manuel de Paula sings it in Mario Maya's 'Ay Jondo'. The cut is labeled 'Taranto y Minera', but the cante in question is sung first - it goes:

    Nadie puede escoger                     No one can choose
    El vientre de donde se nace         the womb from which they are born
    Yo he nacido de una gitana         I was born from a Gypsy
    y bendidta sea su sangre             and blessed be her blood

So, is this melody a minera or a taranto?

The place to look, of course, is to the cante of someone who really specializes in these cantes - Antonio Piñana, who has two albums devoted to cantes del Levante.  Listening to his record, there is a cante called 'levantica' which has this melody - not the things he calls minera nor tarantas/os. The liner notes point out that he interprets the "rarely heard" levantica.

So, if Piñana is taken as the authority (and the labels are not confused), it seems that Camarón, Manuel de Paula, and others are singing levantica - not mineras nor tarantos.

The second verse sung by Manuel de Paula is very similar to a minera sung by La Susi (who has a number of mineras recorded - one on the La Rachí record and another on the Así soy yo). What Susi calls minera seems much closer to what Piñana sings as minera.

What's going on? Looking at the Piñana record, there are several different cantes: tarantas, mineras, fandangos mineros, levanticas, cartegenaeras, malagueñas cartegeneras ... Perhaps only real specialists control the subtle distinctions, while others learn the cantes and call them either tarantas/os, mineras, more or less at random.

Turning to cartegeneras, there seems to be more consistency in the recorded versions I found. Someone mentioned the one on the Archivo anthology by Lebrijano (Al pie de un soberano). Camarón has one recorded on the Canastera record. I also found one by Caixo Sanchez, and two by Piñana. One of Piñana's cartegeneras sound pretty much like the others. The distinguishing characteristic of this cante is that the first line heavily emphasizes the D7 chord (assuming an F# base) - the singer sings the note C - this gives the line an interesting 7th sound that hangs in the air.

Piñana attributes this cartegenera to the famous El Rojo el Alpargatero ('Red the espadrille maker'). He, along with others, such as Pepe el Morato, were instrumental in developing a number of styles of cantes del Levante; this happened at the end of the 19th century, while these artists hung out in a bar in Cartegena. Pohren cites an article by Maria Adela Párraga, where she explains the origin of these cantes. She attributes them to an influx of miners from Jaén and Almería, bringing tarantos that mixed with the 'cantes de madruga' of Cartegena. She suggests that cartegeneras and mineras are the result of this mixture.

El Rojo's son, Antonio Grau Dausset (notice the Catalán/Alicantés name), preserved his father's cante, and taught much of it to Antonio Piñana.

According to Pohren, a student of El Rojo's, La Peñaranda, took the cantes del Levante to the café cantantes, and popularized them. Pohren attributes the following verse to her, which she sang por cartegenera:

    Son las tres de la mañana                 It's three in the morning
    ¿dónde andará ese muchacho?         where could that boy be
    estará bebiendo vino                         he'll be drinking wine
    y luego vendrá borracho                     and then will come home drunk

Lots of people sing a version of this por tarantos (and La Bernarda sings it as a tarantos por bulerías on the Potaje record).

It seems that the cantes del Levante, as we know them, came about in the end of the 19th century in La Unión and in Cartegena, perhaps due to the marriage alluded to by Diaz Párraga, and largely due to the creativity of El Rojo el Alpargatero. Manuel Ros Ruiz, in his Introducción al Cante Flamenco quotes the following from Antonio Piñana:

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(quote attributed to Antonio Piñana)

La Unión ... and Cartegena couldn't have suspected, back in 1885, that a man who had come from Anadalucía, although he was from  Villena (Alicante),  would be the creator of the cantes that today are the pride of the region. This man was El Rojo el Alpagatero, familiar like few others with the cantes andaluces, and possessing the faculties to interpret them, so that he adapted the songs of miners, full of rips and sad cries, to the gitano-andaluz style, creating what today we know as tarantas, mineras, and cartegeneras. El Rojo ... collaborated with other singers of the region and with miners who arrived from Linares and Almería. Today we remember the names of ... (including El Morato) ... A verse expresses all this history:

    Ha llegado un forastero         A stranger has arrived
    a la sierra de La Unión          in the mountains of La Unión
    no trabaja de minero             he doesn't work as a miner
    le llaman en la región            they call him here
    El Rojo el Alpargatero          El Rojo el Alpagatero

Quickly, professional singers like Antonio Chacón added these cantes to their repertoires - also Antonio Grau, El Rojo's son, taught them during his residence in Madrid while studying literature, and later in Russia where he performed until returning to Spain. ... After that, because of the difficulties that the interpretation of these cantes pose, they were corrupted and were left forgotten, except for a few afacionados like El Porcelana and Patricio Alarcón. In 1952 I had the opportunity to meet Antonio Grau, and he taught me various styles of cantes mineros, and he even urged me to revitalize them.

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So it seems that Andalucía came to el Levante, and brought a flamenco spin on the indigenous cantes (which may have been a mix of Jaen/Almeria and La Unión). These were popularized during the café cantante period (probably by people like La Peñaranda), and were taken up by the heavies of the day - Chacón, and probably Manuel Torre. From there, they became part of the standard repertoire of cante flamenco, and are interpreted widely by Gitanos and Payos alike. Purists, such as Piñana, of course, would probably have said that these interpretations are corrupt, and would insist on the versions passed down from El Rojo through his son. Nevertheless, the tarantas that we usually hear most probably come from the Chacon/Torre tradition.