All molecular biology (MB) tool can be employed in functional genomics (FG), as the aim of MB is to identify the function of a certain gene, transcript or protein in a certain organism and / or condition. However, nowadays the majority of the FG studies have been focused on high-throughput tools, such as:
Microarray to evaluate mutations and (earlier) gene expression.
Next Generation Sequencing to sequence genomes, transcriptomes, metagenomEs and many other sets of nucleotide libraries.
Mass Espectrometry to analyze proteins in a sample.
All these techniques depends on complex bioinformatics analysis, and require accuracy statistical validations in most cases.
Molecular Biology exclusively refers to wet lab work, functional genomics uses almost all of the molecular biology tools but adds bioinformatics to it since it usually deals with large datasets.