They are two different things. Assisted Natural Regeneration (ANR) is a way of regenerating forest systems and vegetation using support methods that increase the overall success rate, while near-natural forest management or close-to-natural forest management is closer to an eco-friendly way of treating production forest. The first is about regenerating vegetation, the second one is about forest management for production purposes. See the publications below.
Article Application of Assisted Natural Regeneration to Restore Degr...
Chapter Close-to-Nature Forest Management in Europe: Does It Support...
Toutes les deux il me semble qu'elles produises un effet positif sur la croissance et le développement des espèces forestières. La 2ème nécessite une large vision des opérations (intensification), celle-ci ma foi demande des moyens!