[css] adding css class to multiple elements

You need to qualify the a part of the selector too:

.button input, .button a {
    //css stuff here
}

Basically, when you use the comma to create a group of selectors, each individual selector is completely independent. There is no relationship between them.

Your original selector therefore matched "all elements of type 'input' that are descendants of an element with the class name 'button', and all elements of type 'a'".