What's the history behind this? I am assuming non-Theravada monks eat after noon, and use money. Correct me if I'm wrong.
If I'm not wrong, why do the sects differ in this manner?
They differ for any number of reasons. For one, there are at least five different 'official' versions of the vinaya - each of which is prominent in different countries. The rules in each vary slightly - some have more rules, some have less, some place greater emphasis on different things, etc. A lot of it also has to do with tradition and the culture where Buddhism is practiced. If there is one thing you say about Buddhism it's that it very much malleable to local custom.
A very good example of this is Japan. Some monks there will accept money such as for funeral services. Many will eat after noon, despite the injunction not to - it's just called "medicine" instead of a meal! My own teacher's teacher really loved his sake despite that being a fairly clear violation of the fifth precept. Some Japanese monks, believe or not, even get married.
I think it's helpful not to view Buddhism as a monolithic entity. It really is as complex as the people practicing it.
Bhikkshu Pratimoksha As far as I know (and I verified this with a Chinese Malaysian monk), the pratimoksha is what non-Theravada monks follow. It is more or less the same but has 250 rules over the Theravada 227. The extra rules however, can be found more or less in the Theravada Culavagga or Mahavagga. (Generally known, but I did not verify)
The rule on money is very basic and part of the 10 precepts. The same with eating after 12 Noon. The rule however mentions "gold or silver" as the wording and is defined in the vibhanga as anything dealing with money or trade. I remember once hearing that Mahayana follows a different interpretation of their rules. This may be where it might be "allowable."
A long time ago, in Myanmar, I once traveled with a "vinaya" Mahayana monk from Malaysia. He did not use money. They had two monks in his monastery including himself. It was the only one in Malaysia as far as I could remember (I think I asked him). When we stopped the car to urinate in the forest, he did his business while standing up, which is against the rules. We must squat. I remember asking him about this, and that was where I was told that they follow a different commentary. This commentary seemed to render many of the 250 rules as obsolete. However, this monk did not use money, so I presume that rule was left intact.
I welcome a Mahayana monks to edit this post.
One has to distinguish between monks/nuns that follow a Vinaya and those that do not follow. You may have monks that use such title but cannot be regarded as true monks because they have not been ordained in accordance with, and follow the Vinaya rules.
In the pali suttas the Buddha says that he teaches the Dhamma and Vinaya, i.e. the Doctrine and Discipline. So, it is fair to say that a monk or nun who does not follow the Vinaya rules cannot be regarded as a true Buddhist monk or nun.
A monk/nun which follows the Vinaya is not allowed to eat after midday and to handle money. There are some food items allowed after midday but those are specified in the rules.
Many Chinese Buddhists mistakenly think that Mahayana Buddhism teaches the practice of vegetarianism, and confuse ‘Chi Su’ (vegetarianism) with ‘Chi Zhai’ (not eating after noon until the next dawn). In the early Suttas, ‘Chi Su’ is said to be the unbeneficial ascetic practice of external sects. ‘Chi Su’ is practiced by Han Chuan (Chinese Buddhism), not Bei Chuan (Mahayana Buddhism), since Tibetan and Japanese Buddhists are not vegetarians. Chinese emperor Liang Wu Di commanded Buddhist monks and nuns to eat vegetarian food. The word ‘Zhai’ means not eating at certain hours, i.e. fasting. Thus the Muslim fasting month of Puasa is called ‘Kai Zhai’. The Buddha taught his disciples to ‘Chi Zhai’, i.e. not to eat (with exception of medical allowances) from noon until the next dawn (1 p.m. till 7 a.m. in Malaysia). In Han Chuan this ‘Chi Zhai’ became synonymous with ‘Chi Su’.