ある/持っている

In my textbook it says that both ある and 持っている are used for possession. The specific examples given are テレビがありません and ス－さんはお金をたくさん持っています and, according to the book, both express possession. I'd like to know if there is any difference between using one or the other.

I found this link the other day Learning Japanese is a Wonderful Thing: The word for "have": 持っている vs. には～がある/いる that says ある is used for things you have but don't actually own (the example given is brother) and 持っている for things that you own and can discard any time you want (a mobile phone, a TV...) Would that be an accurate explanation?

持つ can be used also for brothers. (e.g. 出来のいい弟を持つと大変だ。)
As you know, ある means "to exist", thus, テレビがありません basically expresses "there is no TV in a place". For instance, you can say 実家にはテレビがあるけど、今住んでるアパートにはありません。
持つ is volitional(it can be used also for non-volitional cases especially as 持っている, though) and can mean "to hold/carry". That would be the main difference, I think.