Of course not. When we speak of rare coins, we are talking about numismatic rarity, coins that seldom appear for sale or for which a relatively small number of coins are known to exist. However, most numismatists continue to use Sheldon's Rarity Scale for all U.S. Coins, and its conservative assignment of rarity. When we speak of a coin's weight, we refer to its gross weight, the weight determined from simply placing the coin on a scale. Gross weights are useful in the study of Ancient Greek and Roman coins, World Coins struck before about 1800, and coins of the American Colonies as the weight of similar coins within these areas may vary greatly.
Gross weights are less useful on more modern coins as coin production became more uniform.
On the other hand, Fine Gold Weight refers to the amount of pure gold contained in a coin, and is determined by multiplying a coin's gross weight by its fineness, or percentage of gold relative to its total metal content.