Is there any difference between “a ... sense of purpose” and “a sense of ... purpose”?

Solution 1:

Both can mean that everyone has a shared purpose. But a sense of common purpose can also mean that one only thinks everyone has a shared purpose.

So you can build a common sense of purpose within a team. Or you can instill a sense of common purpose into a competitor.

First, look at the nouns being modified:

sense : a meaning conveyed or intended

purpose : something set up as an object or end to be attained

Looking at the grouping:

{common sense} of purpose : {shared understanding} of the goal

sense of {common purpose} : understanding of a {shared goal}

The difference is subtle, but it's there. Same with the second set of phrases:

{spiritual sense} of purpose : {sacred intention} toward some goal

sense of {spiritual purpose} : understanding of a {sacred goal}

The distinction is perhaps less clear in this case, but spiritual is modifying a different noun in each sentence.