I always used "wallet" for both men and women but I was told that it is a mistake and wallet is for men and purse is for women. Checking this information on internet confused me as you can see in the pictures bellow. It seems that wallet can be both for men and women, but in Cambridge dictionary it's written that wallet "is used especially by men". What in fact I have to use?
The question of which word should not be used for which gender is a bit the other way around here. It's the word "purse" that is used exclusively for an object that a woman would carry. Maybe someone decided that if there is a word for "women's things", that women should not be afforded a "man's thing".
The thing is, the word "purse" also means a small bag (and sometimes, not that small a bag). [Edit: this is more of an American English thing, as Sarriesfan points out in the comments.] So using it would introduce ambiguity as to what it is exactly that we are talking about. "Wallet" is a word that more specifically refers to that small object where you could only fit money, cards, and coins, and not really much more than that. A hairbrush could fit into a "purse" [in American English], but it would definitely not fit into a "wallet".
Which is why, where our goal is to specify an object as exactly as possible, and this object appears to be small, it should be a "wallet".
Those people who insist that something that a woman carries must be a purse actually have a preconception of what it is that women must carry. If a woman carries this:
it does not suddenly become a "purse". Women often carry wallets like these, and even minimalist wallets like this one:
Someone's stereotypes about what women are supposed to carry should not preclude us from finding right words for actual objects that they carry. The word "wallet" is a more exact description for something that would not fit, in addition to money, also a hairbrush, a mascara, two lipsticks, and a pocket mirror. That is why both "women's" objects from your pictures can be and are called wallets. One could also describe them as purses, but this is not a must. I would say that if this object requires paper money to be folded, it can't be called a purse, but this is probably my personal view on classifying these things. E. g., here is a thing that definitely requires money to be folded, and yet it's called a purse (and it's really not that different from the second "men's wallet" in your pictures).
A thing which fits paper money that has not been folded can be called a purse and also a "pocketbook" (a more traditional word that is also often used for an object that incorporates a checkbook). But if it it's too small to also qualify as a bag, you can very well describe it is a wallet—and this holds both for American English and British English. E. g., looking at the website of Harrods, which is a UK business, I'm finding two practically identical objects, one of which is called a purse and another a wallet.
Another thing to note is that, since in recent times men (whose "manly" ideal is stereotypically of someone not burdened down with unnecessary trifles) have to carry more things (e.g. a mobile phone or two mobile phones and, say, a powerbank), it is now more common for men to also carry a small bag, and these small bags are sometimes jokingly called "a murse" ("man purse").
However, which style one chooses for oneself is now in no way as determined as it used to be when the society was more traditional. There are women who don't like to be "girly girls", and there are men who do not feel that they become less of a man when they use things that are, um, more whimsically elegant.