There are different versions of the labours, but it isn't a Greek-Roman split: it's more that every account of the labours gives a different list, in much the same way that everyone gives a different list of the 'seven wonders'. Here's a summary of three Greek lists, the second and third being Roman-era, and one Latin-language list:

	Euripides, Herakles 348-411	Diodoros of Sicily 4.11-26	ps-Apollodoros, Library 2.5	ps-Hyginus, Fabulae 30
	5th cent. BCE	1st cent. BCE	1st cent. BCE?	1st/2nd cent. CE?
1	lion of Nemea	lion of Nemea	lion of Nemea	lion of Nemea
2	defeat Centaurs	hydra of Lerne	hydra of Lerne	hydra of Lerna
3	golden-antlered hind	Erymanthian boar	hind of Keryneia	Erymanthian boar
4	horses of Diomedes of Thrace	golden-antlered hind	Erymanthian boar	golden-antlered hind of Arcadia
5	kill Kyknos the bandit	birds of Stymphalia	cattle-yard of Augeas	birds of Stymphalia
6	apples and dragon of Hesperides	stables of Augeas	birds of Stymphalia	stable of Augeas
7	slaying pirates	fetch bull of Crete	bull of Crete	bull of Crete
8	relieve Atlas of his burden	horses of Diomedes	horses of Diomedes	horses of Diomedes
9	girdle of unnamed Amazon queen	girdle of Hippolyte	girdle of Hippolyte	defeat Hippolyta
10	hydra of Lerne	cattle of Geryones	cattle of Geryon	defeat Geryon
11	kill Geryon	rescue Theseus and Peirithoos from Hades	apples of Hesperides	defeat dragon of Hesperides
12	fetch Kerberos	apples of Hesperides in Libya	Kerberos	Cerberus

Some feats that appear in one list appear in other accounts as side-quests: for example the bandit Kyknos, who is one of the main labours in Euripides, is something that Herakles does along the way while performing his eleventh task in ps-Apollodoros. The battle with the Centaurs takes place while on his way to the Erymanthian boar in Diodoros and ps-Apollodoros. And relieving Atlas of his burden of holding up the sky is something he does on his way to fetch the apples of the Hesperides in ps-Apollodoros.

And there are plenty more side-quests too. In Diodoros, on his way to fetch the Cretan bull, he establishes the Olympian games, participates in the Gigantomachy, and releases Prometheus -- just to pass the time. In both Diodoros and ps-Apollodoros he wrestles Antaios and kills Bousiris in Egypt on his way to fetch the apples of the Hesperides. And the list of side-quests in Diodoros' account of the tenth labour goes on for pages; much of it comes from the Greek-Italian historian Timaios of Tauromenion.

These four are probably the best-known lists: Euripides because it's Euripides, and the other three because they're a decent match for one another. But there's no single canonical version either in the Greek pre-Roman world or in the Roman world.