Safe, secure can both mean free from danger or apprehension of danger.
Safe may imply that one has passed through dangers or has run some risk (as of injury or of being lost) without incurring harm or damage or it can apply to persons or possessions whose situation or position involves neither risk nor exposure to destruction or loss or to things (as highways, bridges, or vehicles, or as policies, actions, or courses) which are so constructed or designed that they expose one to few or no risks or to a cautious procedure which keeps one out of danger or free from the risk of making an error or blunder.
Secure in a few idiomatic phrases implies freedom from anxiety or apprehension of danger. In more general use secure tends to stress freedom from anxiety not as merely a subjective state but as a frame of mind induced by grounds that are or appear to be good and sufficient. Sometimes the grounds are intellectual and imply sufficient evidence to establish the certainty of something that has been doubted.
Sometimes the grounds are material, such as the existence of sufficient money, the possession or definite expectation of property, or a definite means of livelihood which enables one to live or make a venture without fear, or the provision of safeguards or protective devices which make a thing safe to use or follow.
Often the term suggests not only a freedom from fear of danger but a position, condition, or situation free from all hazards.