【Adherence】 and 【adhesion】 are usually distinguished in current use.

In spite of exceptions the tendency prevails to use 【adherence】 when mental or moral attachment and 【adhesion】 when physical attachment is implied.

• they gave their 【adherence】 to the cause of reform
• the 【adhesion】 of lung tissues to the pleura

Sometimes, however, 【adhesion】 is used in place of 【adherence】 when the writer feels that the physical connotations of the former will add emphasis.

• the iron force of 【adhesion】 to the old routine
  — Arnold

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