Step 1: Understanding the Question:
We must determine the specific type of structural isomerism existing between methoxyethane and propan-1-ol.
Step 2: Detailed Explanation:
First, let's write out their molecular structures and formulas:
Methoxyethane: $CH_3-CH_2-O-CH_3$. It is an ether. Its molecular formula is $C_3H_8O$.
Propan-1-ol: $CH_3-CH_2-CH_2-OH$. It is an alcohol. Its molecular formula is $C_3H_8O$.
Both compounds possess the exact same molecular formula ($C_3H_8O$) but feature entirely different functional groups (an ether group versus a hydroxyl/alcohol group).
Isomers differing in their functional groups are called functional group isomers.
Step 3: Final Answer:
The isomerism exhibited is functional group isomerism, matching option (C).