It is a good question.

This relationship was well discussed in a report "Concordance, adherence and compliance in medicine taking" done for the National Co-ordinating

Centre for NHS Service Delivery and Organisation R & D (NCCSDO). According to this report:

Compliance is defined as: ‘The extent to which the patient’s behaviour matches the prescriber’s recommendations.’ However, its use is declining as it implies lack of patient involvement.

Adherence is defined as: "The extent to which the patient’s behaviour matches agreed recommendations from the prescriber.’ It has been adopted by many as an alternative to compliance, in an attempt to emphasise that the patient is free to decide whether to adhere to the doctor’s recommendations and that failure to do so should not be a reason to blame the patient. Adherence develops the definition of compliance by emphasising the need for agreement.

Concordance is a relatively recent term, predominantly used in the United Kingdom (UK). Its definition has changed over time from one which focused on the consultation process, in which doctor and patient agree therapeutic decisions that incorporate their respective views, to a wider concept which stretches from prescribing communication to patient support in medicine taking. Concordance is sometimes used, incorrectly, as a synonym for adherence.

This was more clarified in following article: 

http://www.pharmaceutical-journal.com/learning/learning-article/what-is-concordance/10988929.article

Which says: 

Concordance is fundamentally different from either compliance or adherence in two important areas: it focuses on the consultation process rather than on a specific patient behaviour, and it has an underlying ethos of a shared approach to decision-making rather than paternalism. Concordance refers to a consultation process between a health care professional and a patient.

Compliance refers to a specific patient behaviour: did the patient take the medicine in accordance with the wishes of the health care professional? For this reason it is possible to have a non-compliant (or non-adherent) patient. It is not possible to have a non-concordant patient. Only a consultation or a discussion between the two parties concerned can be non-concordant.

I largely agree, certainly never 'compliance', which threatens to rob the patient of his or her autonomy as a rational human being and therefore traverses ethical limits. While concordance remains acceptable, I personally prefer adherence. In the consultation, the clinician should first ask 'Who are you', before asking 'What is wrong?'. The eliitation of narrative and gaining an insight into the richness of the patient's biography should be the fundamental starting point of the clinical relationship. The establishment of the clinical relationship, based on mutual respect, equality and trust' has been shown by both qualitative enquiry and also by empirical studies to set the scene for medication adherence by the patient who, being educated by and trusting the clinician's integrity, adheres to the recommended medication regimen, whether it is simple or complex and this adherence can be the subject of continuing follow-up as part of a wider person-centered approach. In the context of pharmacy, the relationship is not clinical, it is of a different character,, pharmacists do not have patients, though studies published over recent years, not least within the two journals I edit (European Journal for Person Centered Healthcare and Journal of Evaluation in Clinical Practice)demonstrate how an active acquaintance between pharmacists and patient based on the patient's medication needs and concerns, is of central importance in maintaining adherence and thus generating, probabilistically, improved health outcomes. So, for me, the concern is adherence in the context of the question posed, an adherence to the medication regimen that has been agreed between the patient and the clinician in the context of the consultations.