The 70S ribosome is built from two subunits, the 50S and the 30S, and each one offers its own drug-binding pockets. Aminoglycosides such as gentamicin bind the 30S subunit at the decoding site of the 16S rRNA. That site is where the ribosome checks each codon against its tRNA, so disturbing it lowers the fidelity of codon-anticodon pairing: incorrect amino acids get inserted, and translocation is blocked as well. The proteins that come out are misfolded and nonfunctional, and because damaged protein piles up and membrane insertion fails, the aminoglycoside is bactericidal.
Tetracyclines also bind the 30S subunit, but at the A site, where they sterically block the incoming aminoacyl-tRNA from docking. Protein synthesis stops, yet the cell is not immediately destroyed, so tetracyclines are typically bacteriostatic. Macrolides such as erythromycin bind the 50S subunit inside the nascent peptide exit tunnel, so the growing polypeptide cannot move out. Synthesis halts here too, and macrolides are generally bacteriostatic.
The pattern holds: the subunit and the exact site decide whether the drug merely stops translation or also drives the cell to make toxic, misfolded products. That is one reason aminoglycosides kill while tetracyclines and macrolides mainly hold growth in check.