There were two different words used in the New Testament that were both translated as anointing. The first, Chrio, was always limited in its use to the sacred and symbolical anointings which refer to the anointing of the Holy Spirit. The other word translated anointing in the New Testament, is Aleipho, which simply means to smear with oil or ointment. This word for anointing was always used when referring to the cultural practice of anointing.
The cultural practice of anointing was quite common back in Biblical times. Anointing the face or body with oil was a widespread practice among ancient middle eastern cultures. People would regularly smear oil on their bodies and faces to protect the skin from the harsh elements of the climate. They referred to this practice as anointing themselves. The act of anointing people was also observed when someone wanted to honor an important guest or to prepare a body for burial.
There is a very real difference between the cultural practice of anointing, and the anointing of the Holy Spirit. Not understanding this can, and often does, lead to confusion. The cultural practice of anointing is mentioned frequently throughout the Old and New Testaments. You can see this practice in everything from ceremonially anointing kings into office to anointing the sick with oil.
Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord; 15 and the prayer offered in faith will restore the one who is sick, and the Lord will raise him up,… James 5:14-15 NASB
Notice, it is not the anointing with oil that heals the sick. It is, and always has been, the prayer of faith that heals the sick. We must be careful to not mix the cultural aspects of anointing with the anointing of the Holy Spirit. Much of what the modern church attributes to and uses anointing oil for, actually finds its origins in the cultural aspects of anointing. That is, (Aleipho), rather than the anointing of the Holy Spirit, (Chrio).
To know more about the anointing check out the book, Marked by the Anointing, by Anthony Trezza.