Does a character that speaks giant understand/know the meaning of the Giant runes provided in Storm King's Thunder? My guess would be no - the Giant language is based off of the Dwarvish script (PHB p.123), which I don't believe to be the same (Sword Coast Guide p. 105 doesn't look like the runes). Is this the case?
In Storm King's Thunder, the giant runes are used in magical contexts, as in the various magic items, and as nonmagical insignia—kind of like the no symbol or "Ghostbusters thing." They aren't used to write things down. There are a couple places, such as a location described on page 212, where it's made clear that giants do their sentences-and-paragraphs writing in Dethek (the Dwarvish script), not in giant runes. So it looks like the giant runes aren't a full-fledged writing system, and a fluent speaker/reader/writer of giant wouldn't necessarily know them.
There's more compelling evidence, but it is spoilery:
On page 125, Harshnag "is familiar with the ise rune and can identify it; the other runes are unknown to him." The runes in question are those that correspond to the six giant tribes. Harshnag is a frost giant and on page 120 it is expressed in no uncertain terms that he speaks Giant, but apparently this does not mean he knows all or even more than one of the runes.
I'd challenge what the PHB state. The dwarven script is called Dethek, and is widely used by races that hate things dwarven. So there is a point that the Dethek script would be widely disseminated by the dwarves, but not created by them, otherwise orcs and goblins probably would adopt something different.
Given that the giants arrived in Faerun before the dwarves, and the dwarves overthrew the giant rulers after some centuries of fighting, they probably picked up the giant's aplhabet, rather than the other way around.
The runes in SKT are special runes, used to empower the giant's devices. In some places,
defacing the runes causes the devices to fail.
The characters do not know what the runes are even if they speak giant. Not even most NPCs know all of them.
(...) The characters have to figure out which rune is which through trial and error, or with the aid of magic such as the divination spell. A character who has proficiency in the Arcana skill can tell that the runes are magical, but not what the runes mean (...) [pg 125]
Some ancient creatures might know all of them, but they would rather eat the characters than part with their knowledge.