What's the difference between heroism and valiance?

Heroism

Definition:

(n.) The qualities characteristic of a hero, as courage, bravery, fortitude, unselfishness, etc.; the display of such qualities.

Example Sentences:

(1) Koroma said he was “humbled by the dedication” of 35,000 Ebola response workers “whose heroism is without parallel in the history of our country”.
(2) But how about some first-hand heroism over a second-hand table?
(3) Donald Trump's loud mouth got him into trouble, and it will get him out | Jeb Lund Read more Despite Trump’s penchant for controversial comments – including disparaging the heroism of Arizona senator John McCain during the Vietnam war, which led to widespread condemnation within his party – Trump has maintained a substantial lead in national polls for the Republican presidential nomination.
(4) As the toxicology reports come in post-disaster, the facts of a broken tail mechanism and of Washington's indubitable resourcefulness and heroism (possibly coke-fuelled) during the disaster fade into the background as the full extent of his addictions becomes clear.
(5) In The Plague, the stricken protagonists are searching for some way of being human beyond heroism and sanctity.
(6) Part of the fascination here is not just the brittleness, or the basic novelty but the sense of hope in Iceland’s managed miracle, a saga of halls, heroism and meticulous small‑island obsession.
(7) "By making the hero a girl, he took all that macho stuff out of the equation and that gave him the freedom to examine heroism.
(8) Then, as Barnett puts it, there’s the culture of heroism in relief work: humanitarians like to save the day and would much rather do so on their own.
(9) There is a substantial section about the Holocaust .’’ Kaczyński, who engineered his party’s landslide parliamentary election victory last October, has devised a “politics of memory’’ policy that aims to highlight Polish heroism and sacrifice throughout history.
(10) Marie Colvin's tragic death in Syria this week has brought rightly glowing tributes to the heroism of one of the bravest journalists.
(11) They are an outlet for heroism, a reason for lucrative taxation and, with luck, a source of glory.
(12) Kobani was the Kurdish Stalingrad, and its defence became a byword for heroism.
(13) The town’s successful defence became a byword for heroism.
(14) The more astringent sensibility belongs, of course, to Dahl: one born of boarding-school bullying, extreme heroism in the second world war as a fighter ace and the death of a beloved child (to whom he dedicated The BFG).
(15) "But Novodvorskaya's heroism concealed the fact that she was a person with a European education and a talented publicist.
(16) In a nutshell: Persian heroism Israel – The Urburb Welcome to the 'urburbs' ... the Israel pavilion.
(17) It was, he said, "a day to remember all those who lost their lives" on both sides as well as to "salute the heroism of the task force" sent to correct a "profound wrong".
(18) It shows crowds of people cheering the heroism of these new pioneers.
(19) My dad just did what he was trained to do but, under fire, when it's observed, it's called heroism."
(20) Most remain deeply proud of the heroism shown by their colleagues.