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).
