Escape stresses the fact of getting away or being passed by not necessarily through effort or by conscious intent. Definition of avoid verb in oxford advanced learner's dictionary To stay away from someone or something
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To prevent something from happening or to not allow…
Avoid, escape mean to come through a potentially harmful or unpleasant experience, without suffering serious consequences
To avoid is to succeed in keeping away from something dangerous or undesirable To avoid meeting an enemy. To make void or of no effect If you avoid a person or thing, you keep away from them
When talking to someone, if you avoid the subject, you keep the conversation away from a particular topic.