The 'Tax included' distributions can only break out one jurisdiction, so if you require both GST and PST, then it is easier to set both up as 'tax' distributions.

Use the 'purchase' tax type if you want the purchase to show up on the Tax Tracking report (if the company profile is set to include only included details with distribution codes). If a purchase distribution code does not have Tax Tracking enabled, it will not appear on the report.