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Asking how day trading is different from gambling is somewhat like asking how getting lawfully married for an hour is different from prostitution. There is an obvious similarity between the two things, while at the same time the situation surrounding them is somewhat different.

Certainly there are some shared pitfalls between investments and gambling. There is the danger of addiction, losing one's money, obsession with money and losing focus on other things in life, sometimes some ethical questions, and so forth.

At the same time, there are some things that surround gambling that are not usually found with investing, even short-term investing or day trading.

Gambling often has no benefit for society and is often based on a game or wager that will not benefit anyone, such as card games, slot machines, or online apps. (With a few exceptions such as lotteries that fund education) In contrast, the ideal behind investing is that it contributes to a product or business which benefits society. Whether or not day trading fulfills that ideal is another question, but at least the inherent goal is different.

Gambling has often been linked to violence and personal crime.

With investing, one actually gets an asset of value, regardless of how long one keeps it, whereas with gambling, one usually doesn't. So there is an actual sort of trade. 

Casinos and betting shops prey on people who are desperate and already down and are designed to make people lose, otherwise they will not turn a profit. Even in cases where the proceeds from gambling are being used for a greater cause (such as lotteries for education), the system is designed so that the player loses, otherwise there is no point in them running it. Basically it is just another way to extract money from people.

In contrast, the underlying hope behind investing is that the business or product succeeds and that it is a win-win situation, even if, in practice, people lose out, sometimes severely.

If you walk by any place of gambling, or even accidentally end up on one of their sites online, there is often a deep spiritual malaise and a cloud of despair. In some places like Vegas, this is covered up by glitter, underdressed women, and so forth. One doesn't tend to find this in places associated with investing. 

So, these are some of the ways that gambling and investing differ on a deeper level.

Basically it is difficult to be personally or spiritually healthy when being involved in gambling, whereas that seems to be less of a concern for people who work with investments, although of course many things in life can lead to spiritual concerns and one should always be careful.

Anyway, it is always good to think about the ethics and wisdom of what one is doing, and whether or not you personally consider day trading to be ethical is something you have to consider for yourself.

It is also wise to consider the possibility of severe loss and not to put any money into investments (day trading or otherwise) that one can't afford to lose. 

So this is a slightly different approach to the question than a purely shariah answer, hope it provides some useful insights.