is it true that all marble has veins and granites do not? Is this a good way to tell the difference between the two?

No, it is not true. Many marbles do have veins, but there are some that appear to have no veins at all. On the other hand many granites have no veins but there are also those that do have veins. Determining if a stone is marble or granite should not rely on whether it has veins or not. There are several tests you can perform to be sure. A hardness test and an acid test.

Hardness Test: Try to scratch the stone in question with a pocketknife blade. A pocket knife has a hardness of about 6. Marble hardness is 3-5 and granite is between 7-8. If the knife blade scratches the stone you can eliminate that it is marble. Be careful since there are other materials that are as hard as granite. Quartzite and porcelain can posses the hardness of granite.

Acid Test: The acid test will tell you if you a dealing with marble or granite. Marble is composed of a mineral known as calcium carbonate that will react violently to acid. If a drop of acid is placed on marble it will bubble and fizz. If the same acid is placed on granite, it will not react. The best acid to use for this test is a diluted solution of hydrochloric acid also known as muriatic acid. Be careful since the acid will etch the marble.