Is there a word for the most granular parts of currency, eg, cents, pence, etc?

They are usually referred to as the minor units of currency, or minor units for short. This refers to such things as pence - UK, cent USA & Eurozone, centimes Switzerland etc.

According to TFD- change (n)

a. Money of smaller denomination given or received in exchange for money of higher denomination.

b. The balance of money returned when an amount given is more than what is due.

c. Coins: had change jingling in his pocket.

Perhaps specie or the expression in specie. The definition, according to Merriam-Webster:

• money in coin

• in specie : in the same or like form or kind ; also : in coin

Coinage is generally made up to represent portions of a the smallest bill (also called a note) currency. IE: The amount of funds to be issued does not equal a whole bill denomination so coins represent that portion. For example: The smallest Euro denomination in paper note form is 5euro ... someone needing to pay 4euro will use coins to transfer the value. (in limited cases the smallest note/bill denomination is represented with a coin and in paper form...US is an example...in these instances the coins are rarely used.)