What is the difference between the Pythagorean Theorem and Pythagorean Triples?

The first one is a Theorem while the latter is a set of three numbers (i.e. a triple) satisfying the Pythagorean relation.
Specifically the states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides that is
##a^2 + b^2 = c^2##
where ##a## and ##b## are the measurement of the sides and ##c## is the measurement of the hypotenuse.
On the other hand Pythagorean triples are any triple of positive integers ##(abc)## satisfying the Pythagorean relation ##a^2 + b^2 = c^2##. For instance ##(345)## and ##(6810)## since ##3^2 + 4^2 = 5^2## and ##6^2 + 8^2 = 10^2##.