Reference cell atlases powered by single cell and spatial transcriptomics technologies are becoming available to study healthy and diseased tissue at single cell resolution. One important use of these data resources is to compare cell types from new dataset with cell types in the reference atlases to evaluate their phenotypic similarities and differences, for example, for identifying novel cell types under disease conditions. For this purpose, rigorously-validated computational algorithms are needed to perform these cell type matching tasks that can compare datasets from different experiment platforms and sample types. Here, we present significant enhancements to FR-Match (v2.0)-a multivariate nonparametric statistical testing approach for matching cell types in query datasets to reference atlases. FR-Match v2.0 includes a normalization procedure to facilitate cross-platform cluster-level comparisons (e.g., plate-based SMART-seq and droplet-based 10X Chromium single cell and single nucleus RNA-seq and spatial transcriptomics) and extends the pipeline to also allow cell-level matching. In the use cases evaluated, FR-Match showed robust and accurate performance for identifying common and novel cell types across tissue regions, for discovering sub-optimally clustered cell types, and for cross-platform and cross-sample cell type matching.