Which came first, Carroms or Pool ?

The similarities between the games of Carrom and Pool (8-ball billiards) are obvious. Both involve using a striker/ball to knock one of two sets of other discs/balls into pockets.

The primitiveness of carrom equipment compared to billiards equipment would suggest, to me atleast, that the latter was derived from the former. Perhaps even that European colonists, inspired by watching carroms in South Asia, invented billiards ? But Wikipedia and Carrom.org both say that, despite its present-day prevalence in South Asia, the origins of the game are obscure. According to Carrom.org :

Some say it was the invention of the Maharajahs of India, while many in India believe it may have been introduced by the British. Some books on international games include Burma, Egypt and Ethiopia as possible sources, all of which leads us to conclude that, at this time, no-one knows where carrom originated.

And all Wikipedia says about the history of billiards is that the cue was invented in 1735. But Wikipedia does say this about the variant of Billiards known as Carom or Carambole :

Carambole billiards (or carom) is a billiards game developed in the 18th century in France. The game consisted of two white cue balls and a red object ball. The red ball was called carambola after a red fruit.

What ? So the name is of European origin ? Maybe the derivation was in the other direction then ? And then I find this page about the fruit, which says :

This minor crop was introduced to Africa and South America by Portuguese traders but it is believed to have originated in Sri Lanka and the Moluccas.

And this about the origin of its name :

Carambola was originally a Portuguese name, and goes back to the Sanskrit "karmara", which means 'food appetizer'.

The story of cross-cultural fertilization includes this:

To the English living in southern Asia, the carambola was known as the Coromandel gooseberry.

Trust the Brits to totally screw-up a name in its anglicization.

The mystery of the origins of the games remains...