Do grams and milliliters equal the same thing?

No.

• Grams are a measure of mass (weight); whereas
• milliliters are a measure of volume.

However, the two are related by density:

density = mass / volume.

If, and ONLY if, the substance has a density of 1g/ml (= 1 g/cm³) will its mass in grams equal its volume in milliliters.