How to compare transcriptomic profiles of two cell types (single cell RNA-seq)?
You are looking for a way to compare expression profiles between cell types, and your data is counts of genes expressed per cell. Your issue is that the data is highly dimensional. It has as many dimensions as you have genes. To be able find useful information, you must reduce these dimensions using a statistical technique such as Principal COmponents Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), or Multidimensional Scaling (MDS). The result of these analyses is a reduction of your thousands of dimensions to vectors (eigenvectors in PCA) of variance which you can plot against each other in a scatter plot.

I have been working with Single Cell RNA-seq data and have been exploring the difference in gene expression in a certain type of cells between timepoints. Seurat (R package) is a very powerful tool for scRNA-Seq data analysis. 

Here is a a tSNE of my data. I have added the timepoint labels, but you can see that after performing the dimensionality reduction the two different timepoints cluster by their gene expression profiles. I can then use Seurat to see which specific genes are differentially expressed between the clusters and a whole bunch of other fun things.