Half-jacket or semi-jacketed bullet. It was a common early design, as it took no jacket shaping beyond forming a cup. The same open cup (though with a longer cup) was commonly used to make "soft nose" bullets, which were a common commercial design at one time. There are photos of them in F.W. Mann's 1909 book, The Bullet's Flight From Powder to Target. The shorter ones like you have were produced for plinking and small game hunting in much-reduced loads for a hunting rifle. Speer had 100-grain ones in .308" diameter up until twenty or twenty-five years ago, I think. I believe Hornady had them too, at one point. I've forgotten who else. You would load them with modest charges of pistol powder for rabbit or other game your normal .308 W or 30-06 loads would damage beyond usability. Otherwise, they may be handmade as TX Nimrod said.