Nice comparison with the two half-hitches. This is the version known as the rolling hitch ABOK #1729. The other variation you show is also a taut-line hitch - the Magnus hitch ABOK #1736. My preference is for the midshipman's hitch version - ABOK #1855. It doesn't look quite as nice but provides more friction. All three are properly referred to as a "taut-line hitch."
Nice comparison with the two half-hitches. This is the version known as the rolling hitch ABOK #1729. The other variation you show is also a taut-line hitch - the Magnus hitch ABOK #1736. My preference is for the midshipman's hitch version - ABOK #1855. It doesn't look quite as nice but provides more friction. All three are properly referred to as a "taut-line hitch."