'Ponchartrain' has several different tunes associated with it. People who have only heard one tend to find that confusing. The 'Tramps and Hawkers' tune (also used for 'Flora the Lily of the West' and, earlier, 'Caroline of Edinburgh Town') is used in the version of 'Ponchartrain' of which Planxty and, later, Paul Brady, recorded arrangements.

These being well-known nowadays, it is usually that tune that people outside the USA mean when they mention it.