Many numismatist whether a novice or a professional one are often confused or misused the term "rare" in their collectible piece. Just how rare is your rare coins are something that bugs you quite sometimes. Misused of this term will turn a lot of things to happened. Some people exaggerate their collectible possession to be very rare or extremely rare whereas seldom are seem accurate. For example, if you are a seller, and you try to overemphasize the rarity of a certain item, chances are you might ended up a better sale of your goods for not describing it properly if the buyer is a novice or have very limited knowledge towards that certain item. This is unfair to your customer. If you are a buyer then, purchasing an over emphasized goods will led you to overpay. Sometimes not just overpay but an inaccurate information for your goods.
The "rare" word is a very pleasant word to hear for the collectors world since it represents hard to find, very valuable, chance of a lifetime, collector's item and so forth. Yes, this is very true if you really had one that is correctly and properly described.
In the case for the coins, low mintage record doesn't always confirmed to its rarity status. This depends on the number of surviving known pieces. Coins especially old and in precious metal forms had a long history for its status. It passed on from several people and circulates perhaps the whole world. Most of them had been melted to be recoined or for just their intrinsic value. If there is a certain coin for that particular date for example had been melted in huge quantities either by the mint or private firm and the remaining pieces for that actual mintage is relatively low, then we can conclude that particular coin to be either scarce or rare. This again depends on the number of surviving pieces. Here are the following rarity scale chart for us to better understand:
R8= 1-3 known (estimated), "unique or nearly unique"
R7= 4-12 known, "extremely rare"
R6= 13-30 known, "very rare"
R5= 31-75 known, "rare"
R4= 76-200 known "very scarce"
R3= 201-500 known "scarce"
R2= 501-1250 known "uncommon"
R1= over 1251 known, "common"
This rarity scale also helps us properly described the rareness of a certain collectible pieces especially coins. Banknotes and other numismatic item have their own rarity scale which may not apply to this chart.
So speaking to a 1906-S peso rarity scale, I would correctly rate it as "R3" known as scarce. This is because that the estimated number of survival is between 500-750 pieces are still extant. The reason for collectors dubbed the 1906-S to be rare is because the number of surviving pieces are mostly in the hands of collectors. Once it is in the hands of collectors, it seldom came out for sale again. And the number of pieces which are still to be discovered by collectors are relatively few that's why its been called "rare". Popularity also plays a part.
For the Manila 1828 counterstamped coin of the Philippines, I would rate it as "R4" very scarce since an expert on this field told me that about 200+ pieces are still to be found. For the Manila 1830, the rate would be "R6" very rare" because experts again estimated the surviving pieces would be around 25.
Before I will end this topic, please bear in mind that there is a big possibility of a once "rare coin" will downgraded to a scarce rating or so because there might be a future huge discovery of that particular date of a coin. This already happened on the case of the sunken ship SS Central America which was discovered in 1989.