Step 1: Understand the question.
We compare ethoxy ethane ($C_2H_5\text{-}O\text{-}C_2H_5$) and methoxy propane ($CH_3\text{-}O\text{-}C_3H_7$). We must name the kind of isomerism between them.
Step 2: Check the molecular formula.
Both have the formula $C_4H_{10}O$. Same formula but different structure means they are isomers.
Step 3: Check the functional group.
Both have an oxygen joining two carbon groups, so both are ethers. The functional group is the same.
Step 4: Look at the alkyl groups.
The first has ethyl on both sides. The second has methyl on one side and propyl on the other. So the alkyl groups around the oxygen differ.
Step 5: Name the isomerism.
When the functional group is the same but the alkyl groups on either side differ, it is called metamerism.
Step 6: Choose the answer.
These are metamers, which is option 2.
\[ \boxed{\text{Metamers}} \]