If two solid substances looked the same what measurements and which tests would you perform to determine whether they are actually the same?

Similar-looking matter can have different properties. Some of these tests could be density: find the volume and mass of your substance (displacement test and balance) then determine density with the formula m/v=d. If the density is different, the substances are not the same. 

If you can get your hands on some acid (but don't actually touch that acid, that would burn you) see if the substance will react with it. If one doesn't react, or one reacts differently, they are not the same.

You can also try scratching the solid, to see if their hardness is the same.

There are so many different tests, just keep in mind that chemical and physical properties are both important to determine what matter is.