In basic algebra, their meaning is equivalent, with both denoting multiplication.
When writing by hand, it is common to use * or parentheses (e.g. (2x)(4y)=8xy) to denote multiplication rather than xx as it is easy to confuse xx with x without very precise handwriting. As one progresses in mathematics, it is standard to see xx used less and less in comparison to * or omitting a symbol altogether for denoting multiplication.
In more advanced courses, the meanings of * and xx may differ depending on the context. For example, in vector calculus, * denotes a dot product and xx denotes a cross product. In abstract algebra, xx may be used to denote a direct product. For example, RRxxRR is the set of all ordered pairs (x, y) where x and y are in RR (the set of real numbers).
