The symbol used to denote multiplication, i.e., denotes times .
The symbol is also used to denote a group direct product, a Cartesian product, or a direct product in the appropriate category (such as a Cartesian product of manifolds when it is implied that the smooth structure is the natural product structure.) The similar symbol is reserved for a tensor product, which may rear its head in several guises, representations, bundles, modules.
Portions of this entry contributed by Todd Rowland
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Rowland, Todd and Weisstein, Eric W. "Multiplication Sign." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultiplicationSign.html