Catalyzes the attachment of serine to tRNA(Ser). Is also probably able to aminoacylate tRNA(Sec) with serine, to form the misacylated tRNA L-seryl-tRNA(Sec), which will be further converted into selenocysteinyl-tRNA(Sec). . This is the function of SARS2 (seryl-tRNA synthetase 2, mitochondrial, ENSG00000104835).