Indifference curves and preferences?
A nerd loves both mathematics and physics equally, and hates sports and drinking beer equally.

A football player hates both mathematics and physics equally, and loves sports and drinking beer equally.

The nerd and the football player have the same indifference curves, but not the same preferences.

The point is this: Both agree on the "grouping" of things. But they disagree in the ranking of the groups.

Your Example

If you look at Jim and Pat, they have exactly inverse utility functions and hence inverse ranking in their preferences.

That is, if for Jim $A &gt; B = C = D &gt; E$, Pat will have $A &lt; B = C = D &lt; E$. Both agree on the three groups, but disagree on the order. Jerry's just a monotone transformation (poor Jerry).