This section concerns the ceremonies of reception as a Knight Templar within the Catholic Order. Rules 657 to 686 conclude the Rule of the Temple.
Paraphrased from the book by J. M. Upton-Ward which translated the Templar Rule from the French to English.
See rule 274 and its comments, under Section 3, Penances, for a formula for a profession used by the Templars. Stated simply "Profession" was a way to receive Templar members. "Reception into the Order" was a way to ordain a brother into the spiritual service of the Templars.
Hence there is an "external" aspect to the Templars and an "internal" aspect to the Order. Those who are members, and those who are ordained to serve.