Step 1: Examine the letter positions.
\[
\begin{aligned}
\text{YDEUZ} & : 25,\;4,\;5,\;21,\;26
\text{ASHBR} & : 1,\;19,\;8,\;2,\;18
\text{OZPEQ} & : 15,\;26,\;16,\;5,\;17
\text{AXCMF} & : 1,\;24,\;3,\;13,\;6
\text{HLXEF} & : 8,\;12,\;24,\;5,\;6
\end{aligned}
\]
Step 2: Look for consecutive alphabet pairs.
• YDEUZ: D(D) and E(5) are consecutive; Y(25) and Z(26) are consecutive.
• ASHBR: A(A) and B(B) are consecutive; S(19) and R(18) are consecutive.
• OZPEQ: O(15), P(16), and Q(17) occur consecutively.
• HLXEF: E(5) and F(6) are consecutive.
• AXCMF: A(A), X(24), C(C), M(13), F(6) contain no pair of consecutive letters.
Step 3: Identify the odd group.
All the groups except AXCMF contain at least one pair of consecutive alphabet letters. Therefore, AXCMF is different from the others.
\[
{\text{AXCMF}}
\]
Hence, the correct answer is Option (D).