King's Magic is the kind of magic where true oaths can bring back the dead and your magic item only responds to those of your blood and oaths of allegience create brotherhoods whose unity grants them power. It might involve fated companions and is often focused through marks of authority. It can involve influence of followers, and those under your jurisdiction or whom you have mastered by force of arms. It could involve your lands health and prosperity being attached to yours like ancient Celtic Kings. It might include Fate and Destiny manipulation and it's price is often marked in units of charity or karma.
Bloodline magic is an age old concept far older than its association with D&Ds sorcerors (which is indeed akin to the Daemonic heritage of Merlin and other spell caster's). In fact the idea of being descendents of Dragons and Gods, Daemons and Fae with heralded and strange birth is a common element of many classic heros and legendary/historic kings alike.
From the ancient greek - hero which largely meant half-god to the royal lines of many real world places which attribute there kingship and nobility with blood of Dragon's and Gods to those like Aragorn who invokes his bloodline to great and epic effect more than once in Tolkein's chronicles to In Arthurian Legend you have Galahad/Lancelot blood descendents of Joseph of Arimethea who's skin turns aside thorned plants and resists boiling heat with confidence to Gawaine and his family bearing a fae blood-line granting a gift of sun born strength each with empowered and awakened blood.
In the ancient world oaths were things of "magic" from which power flowed yet made to sovereign rulers as often or more than deities
This magic is not that of a spell caster in any classic sense and is more subtle than any sorcery. It is the Magic when Uther smashes caldwych/excalibur in to the stone and declares only he and his will have it. Its the magic which causes Aragorns hand to catalyze a weed in to a healing herb. Its the magic when the bearer of the Sword of Truth drives his companions in to a berzerkergang. Its the magic which causes Arthurs enemies to crown him king inspite of there own desires and it's focused through his famous Sword of Kingship and again Aragorn calling in the oaths of the unforgiven dead.
In a world where oaths are bindings of magic it is warlords who are the creators of paladins and shamans the creators of spirit warriors.
Oaths are featured in the new martial practices This is to better invoke myth and legend but also creates a world concept touched by history.
Scions of Ancient Bloodlines: Being of a special blood-line often has benefits though they are not necessarily "realised" but rather dormant til awakened.
Awakening / Fosterage - sometimes its on purpose and sometimes its by providence but it is a fact that Heroic Blood is more often Awakened to discover its gifts when raised outside their immediate family or atleast by family that is not themselve awakened heritage (some say that the empowered parentage overshadows an ofspring supressing their expression).
Mark's of Authority Blood-line rites are often enhanced with marks of authority and personal crests through which the scions evoke their own personal power and which symbolise the practicioners family and personal identity.
The Primaries: Dragons, Divinities Daemonics and Fae constitute the primary bloodlines of myth and legend.(In fact each of the main characters from Arthurian tales feature these blood-lines).
Specific blood-lines generally show tendences, and styles even if there is no actual restrictions, for instance Fae blooded heros might have ancient learning, agelessness and gifts involving illusions but not necessarily.
The Blood of Adam: At some level we are all related and in that truth lies a blood-line common to all humans - it is considered divine or by many in the image of the divine and features free-will and dominion over beasts the power of naming and immortality of the soul.(in heroic manifestation see reincarnation and reincarnative memories) and long livedness.
In fact in game terms it takes no special feat to have a special "blood-line" this is fundamentally an aspect of background under player control. However control over the gaining of blood-line gifts can be excercised via rites or the various benefits which can be associated with your blood-line that may take a little more