A set is a collection of objects. In mathematics, they are distinct objects. In common usage, a set is a collection of objects, usually having one or more common attributes: A chess set is collection of objects that are to be used together; a set of books may be all on the same topic; a set of knives may be a collection of knives for different special purposes.
However, with cards, set may also refer to a collection of cards of the same rank. But, in this case, the set you referred to in your example is more properly called a deck (which you already called it).
Another choice is assortment, which is a mixed collection. A standard deck of playing cards is an assortment (a mixed collection) of cards of four suits and thirteen values.
And, of course, the words collection and group are suitable here, as well as some of their many synonyms.