There are two kinds of changes: physical and chemical. Physical properties can change without changing the substance, while chemical properties do change the substance.
Physical properties, like you said mass or texture, can change without changing the substance because the properties don't change the fundamental state of the subject; it doesn't change anything like atoms or molecules.
For example, when you freeze water to make ice, it's a physical change. The water goes from a liquid state to a solid state. But, the substance isn't changed: the compound is still H2O whether it's water or ice.
Another example would be cutting a cake. You make a physical change by cutting a slice out of the cake: you make it smaller. However, afterwards, the cake is still a cake. You didn't turn it into a pie or a muffin; it stayed the same thing, a cake, while just getting smaller.
