"Algebraic data types" refers to having both product and sum types, where products are the records/structs that just about every language has, and sums are indeed the "discriminated unions" under discussion.

Most languages don't have built-in syntax for sum types, so most developers are familiar with sum types only by the shadows cast by a variety of encodings. One of them is the subject of the OP, the Visitor pattern. Another is the "tagged union" seen in C, effectively:

    struct Rectangle { int x, y, w, h; }
    struct Circle { int x, y, r; }

    struct Shape {
      enum {
        RectangleTag,
        CircleTag,
      } tag;

      union {
        struct Rectangle rectangle;
        struct Circle circle;
      };
    };

Which doesn't look too bad until you realize I haven't explained how to use the thing, and then it's similarly involved and even more delicate than the Visitor pattern.