Two things. Audit is a statutory requirement while consulting is not. But if you understand the way an external audit works, you will find a lot of similarities. I'm listing out some of these similarities but I could be totally wrong as I've never worked in consulting so most of this is based on what I've read about consulting.
1) Risk Assessment at the Audit Planning stage: Very similar to consulting engagements in that you identify the key risk areas and then decide how you're going to respond to those (either by increasing internal controls testing to see everything's working efficiently or if they are weak, by increasing the substantive testing to substantiate the transactions, balances and disclosures to see how the management arrived at those). Now this isn't exactly identical to consulting but from what I've read, consulting is about problem solving. You're given a problem, such as cash flow problems, and to solve that, you have to understand the operations of the client and identify risk areas (here though the focus is more on business risk rather than audit risk).
2) Internal Controls Testing: In an audit, you have to document internal controls via flowcharts/narrative notes/questionnaires/discussions with the management to identify possible deficiencies. In consulting engagements, you have to do the same and make recommendations if something isn't working out such as insufficient controls which make them susceptible to fraud as a result of human collusion or too many unnecessary controls which could be causing the cash flow crunch. As far as I understand, both auditors and consultants redesign the controls and make recommendations (as they are not responsible for direct implementation).
The key difference that I see here is the focus of the auditor on audit risk which is the risk of expressing a wrong opinion as a result of material misstatement, which is essentially a function of inherent (pertaining to the nature of the client), control and detection risk, while consulting is more about business risk.
But nevertheless, there are similarities and I see transferable skills (could be wrong?) and both of these professionals do not have to specialize in the subject matter that they're given and cover wide range of sectors and functions. Both provide an impartial and unbiased view. So shouldn't this make the transition from audit to consulting possible and smooth since they're so alike?
Again, I could be totally wrong but as I've mentioned earlier, I haven't worked in consulting so I'm open to any inputs, especially from those working/worked in consulting.