Many approaches have been proposed for identifying cell types.
They usually involve distinguishing characteristics like cell morphology (shape) and their particular function.
The molecular components of a cell provide many more characters for such an analysis.
Over the last few years there has been a technically driven revolution in the analysis of cell types.
This involves, in its ideal form, sequencing all of the mRNAs in cells in a small organisms like a flatworm, a microscopic round worm, a zebrafish embryo or a frog embryo. Using molecular biology tricks (AKA clever techniques), the transcripts that originated from the same cell can be identified, grouped together, and analyzed.
The idea, with respect to cell types, is that a cell type is distinct from other cells types because it is expressing a different cell of genes (which is reflected and detected in its RNA transcripts).
In addition, these techniques allow the development of the cell types to be "followed" over time in a series of snapshots, showing developmental "paths" of the development of a cell type.
Sadly, not much of this is in open access sources yet.