Advances in single-cell RNA-sequencing (scRNA-seq) provide an unprecedented window into cellular identity. The increasing abundance of data requires new theoretical and computational frameworks for understanding cell fate determination, accurately classifying cell fates from expression data, and integrating knowledge from cell atlases. Here, we present single-cell Type Order Parameters (scTOP): a statistical-physics-inspired approach for constructing "order parameters" for cell fate given a reference basis of cell types. scTOP can quickly and accurately classify cells at a single-cell resolution, generate interpretable visualizations of developmental trajectories, and assess the fidelity of engineered cells. Importantly, scTOP does this without using feature selection, statistical fitting, or dimensional reduction (e.g., UMAP, PCA, etc.). We illustrate the power of scTOP utilizing a wide variety of human and mouse datasets (both in vivo and in vitro ). By reanalyzing mouse lung alveolar development data, we characterize a transient perinatal hybrid alveolar type 1/alveolar type 2 (AT1/AT2) cell population that disappears by 15 days post-birth and show that it is transcriptionally distinct from previously identified adult AT2-to-AT1 transitional cell types. Visualizations of lineage tracing data on hematopoiesis using scTOP confirm that a single clone can give rise to as many as three distinct differentiated cell types. We also show how scTOP can quantitatively assess the transcriptional similarity between endogenous and transplanted cells in the context of murine pulmonary cell transplantation. Finally, we provide an easy-to-use Python implementation of scTOP. Our results suggest that physics-inspired order parameters can be an important tool for understanding development and characterizing engineered cells.