What exactly is a mole?
The first thing to realize is that "mole" is not a mass unit. It is simply a quantity - a number - like dozen or gross or score. Just as a dozen eggs is 12 eggs, a mole of glucose is $6.02 \times 10^{23}$ glucose molecules, and a mole of carbon atoms is $6.02 \times 10^{23}$ carbon atoms. "Moles" are only associated with mass because individual objects have mass, and thus a mole of objects also has a certain mass.

So why $6.02 \times 10^{23}$? What's so special about Avogadro's number? Well, nothing, really, it just makes calculations work out nicely. Avogadro's number is defined as the number of $\ce{^{12}C}$ atoms which weigh 12 g. So it's effectively a ratio: how many times larger is a gram than an atomic mass unit? If you have one atom of $\ce{^{12}C}$, it weighs 12 amu. If you have $6.02 \times 10^{23}$ of them, they weigh 12 g. If you have one molecule of glucose, it weighs 180 amu (or thereabouts). If you have $6.02 \times 10^{23}$ of them, they weigh 180 g (or thereabouts). -- This is just like if one egg weighs 60 g (on average), then a dozen of them weigh 720 g (on average), and if one cup of flour weighs 120 g (on average), then a dozen cups of flour weigh 1440 g (on average). The only difference is that dozen is defined forwards ("a dozen is twelve"), whereas a mole is defined "backwards" ("a dozen is the number of 60 g eggs that are in a collection of eggs that weighs 720 g.")

This convenience definition - pegging the value of Avogadro's number directly to the difference in scale between the amu and the gram - is what is probably throwing you. Moles are not a mass unit, but the definition is intimately tied to mass units. The equivalence in numbers at the atomic scale (amu) and at the macroscopic scale (grams) can also result in chemists playing fast and loose with terminology, quickly working back and forth from atomic to macroscopic scale, without a necessarily clear distinction between the two.