It looks weird to you because of the convention of two variables side-by-side meaning "multiply".
First, rewrite the boolean multiplicative (AND) distributive rule, the "x(y+z) = xy + xz" one that looks normal to you, as follows:
x * (y + z) = (x * y) + (x * z)
Now, you can see that the boolean additive (OR) distributive rule is exactly the same in form as the multiplicative one above, just with the "+" and "*" symbols swapped. It looks like this:
x + (y * z) = (x + y) * (x + z)
This should clear up why these two distributive properties are really the same property. Also, don't forget that the "+" here does not mean add. Boolean AND (*) is more similar to our familiar arithmetic multiplication than boolean OR (+) is to arithmetic addition. You can see this by the fact that all the statements made by the truth table for AND (*) are also valid in arithmetic, using "*" to mean multiply. This is not true for OR (+), as 1 + 1 does not equal 1 in ordinary arithmetic.
See what I mean about the boolean truth tables:
0 * 0 = 0 -----> true in boolean and arithmetic
0 * 1 = 0 -----> true in boolean and arithmetic
1 * 0 = 0 -----> true in boolean and arithmetic
1 * 1 = 1 -----> true in boolean and arithmetic
0 + 0 = 0 -----> true in boolean and arithmetic
0 + 1 = 1 -----> true in boolean and arithmetic
1 + 0 = 1 -----> true in boolean and arithmetic
1 + 1 = 1 -----> not true in ordinary arithmetic
It is this difference for OR (+) that makes the identity false in ordinary arithmetic, while the corresponding AND (*) identity is true.