It goes without saying that like all prescription drugs which have been proven safe, chloroquine should only be taken when prescribed by a doctor, at the recommended dosage. Obviously if you self-medicate with any safe prescription drug, you risk harming yourself by overdosing.
I don't think it's a good idea to take the President's happy talk at face value, but then I also didn't think it was ever a good idea to spend money on Trump University, or donating to Trump charities; on the other hand, enough people did that the matters ended up in court and the two branded entities mentioned above were both found to be liable for misinforming their customers/donors.
There are a lot of stupid folk among the public, and it is to them that scam artists like Jim Bakker or Alex Jones market quack cures. There's an appetite for quack cures because they seem affordable relative to the often-inaccessible costs of basic medical treatment, because we don't have a universal public health system in the USA. The sad fact is that people sell snake oil because there are fat profits to be made by doing so, even though most of us recognize such products as little better than placebos at best or dangerous at worst.
This is why we have product regulation, credentialing and so on; it's hard for people to personally assess the quality of every product or service and there are unscrupulous people who are willing to exploit that difficulty.
He's talking to a broad, panicked audience and anyone doing so ought to choose their words carefully. Something like "Great news is that we've already had safety data for this stuff, so we're going straight to efficacy trials!" would convey plenty of optimism without encouraging yahoos to do dumb things.
This doesn't mean it's safe to take, it just means that taking it as prescribed is believed to lead to better outcomes than trying to survive Malaria without taking it.
There's any number of things that chemotherapy or radiation might help with, but unless it is terminal cancer, chances are you are better off without those treatments.
In medical terms, 'safe' is almost always relative. Tylenol is 'safe', and yet it kills many people every year.
Instead, it says: "Do not take more than your recommended dose. An Advil overdose can damage your stomach or intestines. Use only the smallest amount of medication needed to get relief from your pain, swelling, or fever."
People come up with crazy, brain dead ideas all the time. There are flat earthers for crying out loud.
I'm not sure the difference between this and the dosages and chemical makeup of the actual drug being touted by Trump but I imagine anyone with a lick of sense would avoid consuming chemicals designed for fish tanks.
Both counterions get used in medicines, but it's tough to say in general if it matters: sometimes it makes a difference, other times it's just whatever's easier/cheaper to make.
Edit: Yes, I realize what he probably meant. I know how meds work. I still think he should have chosen his wording more carefully.