Independence in appearance is how independent the auditor appears to outsiders such as users of financial statements.
Independence in fact refers to whether the auditor has maintained an attitude of independence throughout the engagement.
For example, an auditor could possibly maintain an attitude of independence in fact even though he or she held shares of stock in a company and performed the audit (the auditor would have violated Rule 101). However, the auditor would not likely be independent in appearance in such a situation. Both independence in appearance and fact are essential and the Code of Professional Conduct concerns both.