Sixty percent of papillary thyroid cancers (PTCs) are driven by BRAFV600E, a mutation associated with high inter- and intra-tumoral heterogeneity. PTCs may become highly aggressive anaplastic thyroid cancers (ATC). While single cell transcriptomics may resolve this heterogeneity, it is potentially confounded by batch effects whose correction may dampen inter-tumor variations. We profiled ATCs and BRAFV600E PTCs with single nuclei RNA-seq and spatial transcriptomics, and an experimental design disentangling biological and technical variations. It reveals that much transcriptional variation in cancer cells and several immune cell types is idiosyncratic, i.e. tumor-specific. It is associated in some cases with genomic aberrations and global tissue states like hypoxia. Beyond idiosyncrasies, differentiation markers SLC5A5 (NIS), TPO, TG and TSHR are lost in a sequence mirrored by their gain during human thyroid organoids maturation, suggesting a new classification of cancer cell states. PTC cells retain TSHR expression and show features of partial EMT with a massive expression of FN1, which promotes proliferation via an autocrine loop. In contrast, ATCs undergo full blown EMT, with expression of mesenchymal extracellular components and loss of TSHR. Finally, we show that the microenvironment of cancer cells is driven by inflammation. These findings may help future stratifications of BRAFV600E PTCs.