Answer
Barium Sulfate [tex]\text{BaSO}_4[/tex] is chemically stable and safe for human consumption.
Barium Sulfide [tex]\text{BaS}[/tex] is toxic and shall be handled with care.
Explanation
Barium ions [tex]\text{Ba}^{2+}[/tex] ions can damage cell membranes and are thus toxic to the human body.
Barium ions in barium sulfate, however, are held tightly in ionic lattice and barely dissolve in water. Barium sulfate thus stay intact and give rise to no harmful [tex]\text{Ba}^{2+}[/tex] ions when orally ingested.
Barium sulfide can dissolve in water at significant quantities to produce barium [tex]\text{Ba}^{2+}[/tex] ions and sulfide [tex]\text{S}^{-2}[/tex] ions. Barium ions are toxic aforementioned whereas sulfide ions can undergo hydrolysis to produce hydrogen sulfide, a weak acid that evolves and behaves as a toxic gas.
[tex]\text{BaS} \; (s)\to\text{Ba}^{2+} \; (aq) + \text{S}^{2} \; (aq)\\\text{S}^{2-}\; (aq) + 2\; \text{H}_2\text{O} \; (l) \rightleftharpoons \text{H}_2\text{S} \; (g) + 2 \; \text{OH}^{-} \; (aq)[/tex]
