Recommender systems have been widely used for various scenarios, such as e-commerce, news, and music, providing online contents to help and enrich users' daily life. Different scenarios hold distinct and unique characteristics, calling for domain-specific investigations and corresponding designed recommender systems. Therefore, in this paper, we focus on food delivery recommendations to unveil unique features in this domain, where users order food online and enjoy their meals shortly after delivery. We first conduct an in-depth analysis on food delivery datasets. The analysis shows that repeat orders are prevalent for both users and stores, and situations' differently influence repeat and exploration consumption in the food delivery recommender systems. Moreover, we revisit the ability of existing situation-aware methods for repeat and exploration recommendations respectively, and find them unable to effectively solve both tasks simultaneously. Based on the analysis and experiments, we have designed two separate recommendation models -- ReRec for repeat orders and ExpRec for exploration orders; both are simple in their design and computation. We conduct experiments on three real-world food delivery datasets, and our proposed models outperform various types of baselines on repeat, exploration, and combined recommendation tasks. This paper emphasizes the importance of dedicated analyses and methods for domain-specific characteristics for the recommender system studies.