What are the key differences between internal auditing and external auditing?

You should be able find a more complete list in your textbook. I think internal audit is WAY more fun than external audit. The external auditors issue an opinion on the fairness of the financial statements taken as a whole. The internal auditirs are regular employees of the company they audit. Internal audits generally examine internal controls and the main purpose is to recommend improvements in efficiency and operational effectiveness. The materiality level for an internal audit is much lower than for an external audit. An external auditor will never examine petty cash, but an internal auditor will. The external auditors are organizationally independent - they work for a completely different company than the company being audited. The also get paid more - the internal auditors receive their regular salary, regardless of their findings. The external auditors get paid based on their contract which includes expenses, overhead and profit. The external auditors issue an opinion on the fairness of the financial statements taken as a whole. The internal auditors may issue an opinion on a much smaller unit they may be auditing, but often they do not. External auditors are required to follow generally accepted auditing standards ( or international auditing standards), internal auditors do not. The internal audits may follow GAAS, they may follow IIA standards, or they may not follow any special standard. An internal audit may cover a time perior of a week, month or quarter. An external audit generally covers a year. You need an external audit every year because you have a new set of financial statements every year, and the internal control environment may have changed since the last audit, creating opportnities for inaccuracies and fraud to make the financial statements inaccurate or misleading. Good internal auditors are like independent efficiency consultants and good managers look forward to having then provide their services. External auditors don't provide much of real value to the line management of a company. Internal auditors may charge the department they audit an internal charge, but often the manager can request their services for free.

Internal Auditing is made by the Organization staff, and the external is made by an outside company or professional, totaly independent without any relation with the organization

Internal Auditing is a perudical auditing done inside the company by the accountants, external auditing are done by outside accounting consultant usually evey year.

I think the general difference is that internal audit is checking how employees are following company's procedures, while external audit is checking company's financial reporting.

The basic difference is internal auditors are company's own employee while external auditors are from outside Audit firm. Their scope of audit is always different. 

However, both are regulatory requirement, while their audit framework and matrices are different.