H&E stain is a popular staining method in histology. Its a combination of two dyes: the basic dye (hematoxylin) and the alcohol-based dye (eosin). In an H&E stain you will usually see both eosinophilia and basophilia: the nuclei of cells basophilic (blue), while eosinophilia is typical of cytoplasmic constituents (pink).
Immunohistochemistry is a method of detecting the presence of specific proteins in cells or tissues. It is widely used in basic research to understand the distribution and localization of biomarkers and differentially expressed proteins in different parts of a biological tissue.