Sequential recommender systems (SRS) have become a research hotspot due to its power in modeling user dynamic interests and sequential behavioral patterns. To maximize model expressive ability, a default choice is to apply a larger and deeper network architecture, which, however, often brings high network latency when generating online recommendations. Naturally, we argue that compressing the heavy recommendation models into middle- or light- weight neural networks is of great importance for practical production systems. To realize such a goal, we propose AdaRec, a knowledge distillation (KD) framework which compresses knowledge of a teacher model into a student model adaptively according to its recommendation scene by using differentiable Neural Architecture Search (NAS). Specifically, we introduce a target-oriented distillation loss to guide the structure search process for finding the student network architecture, and a cost-sensitive loss as constraints for model size, which achieves a superior trade-off between recommendation effectiveness and efficiency. In addition, we leverage Earth Mover's Distance (EMD) to realize many-to-many layer mapping during knowledge distillation, which enables each intermediate student layer to learn from other intermediate teacher layers adaptively. Extensive experiments on real-world recommendation datasets demonstrate that our model achieves competitive or better accuracy with notable inference speedup comparing to strong counterparts, while discovering diverse neural architectures for sequential recommender models under different recommendation scenes.