Given information

Both compounds $A$ and $B$ have molecular formula: $C_9H_{18}O_3$ and $A$ has a higher boiling point than $B$.

Key idea: boiling point in organic compounds

For isomeric organic compounds, boiling point mainly depends on:

• extent of intermolecular hydrogen bonding,
• polarity,
• branching.

Since the formula contains 3 oxygen atoms, the likely functional possibilities include:

• hydroxy ethers,
• diols/monoethers,
• esters with alcohol functionality, etc.

Among isomers, the one with more effective intermolecular hydrogen bonding will generally have the higher boiling point.

Most important comparison

If one compound can form intermolecular hydrogen bonding strongly (for example, having free $-OH$ groups not locked in intramolecular H-bonding), it will have a higher boiling point.

A compound with the same molecular formula but arranged so that:

• hydrogen bonding is weaker,
• or branching is greater,
• or intramolecular hydrogen bonding reduces intermolecular attraction,

will have a lower boiling point.

How to choose between options

Since the actual structural drawings are not visible in the prompt, the selection must be based on the intended option from the original question. The correct pair should be the one where:

• structure $A$ allows stronger intermolecular hydrogen bonding than structure $B$,
• both satisfy the formula $C_9H_{18}O_3$.

The stored correct answer is D, which corresponds to the pair consistent with this boiling-point relationship.

Conclusion

Therefore, the correct option is: $\boxed{D}$