Yes, you can find some size differences between brands. You can even see that the same brand can stock models that differ in size.
We recommend you to always verify what is the size equivalence of the product you are interested in, in its American and European sizes. It could happen that you may always wear 5US men and by mistake, you might be selecting a 5US woman. By verifying the equivalence in the European sizing system or in centimeters, you will not run that risk.
If any specific model fits in a particular way, we try to include this information on the product description. If you have any other specific questions about how a model fits, please get in contact with our Customer Service Department and we will do our best to help.