Most samurai have very unique calligraphy signatures. These are called 花押 (kaō), literately "flower signate". They are highly stylized and very unique in design and shapes. A lot of them don't even contain the signer's name (Hideyoshi's is a single, now archaic, character for "every"). Daimyōs would have scribes write the letter, then just sign it with a kaō. The unique nature of the signature makes it official. According to one story, Date Masamune got in trouble with Toyotomi Hideyoshi for trying to support an Ikki revolt. Hideyoshi had gotten his hand on the letter Masamune sent, with his stylized bird-shaped signature. Masamune got away with it because he insisted the signature for the letter going to the Ikki was fake because in the real signature he pokes a hole with a needle where the bird's eye is. However, none of his signature kept by Sendai museum has a needle hole in it, plus considering the nature of the crime, if the story is true Masamune was probably lying out of his ass and Hideyoshi just let it slide.
Seals slowly became popularized in the Sengoku, especially among Eastern daimyōs, as a replacement for the kaō. The process continued through the Edo and into the early modern day. Seals were also of unique design and often not containing the name of the person using it (Nobunaga's seal, for instance, says Tenka Fubu), and some don't even contain words (the Kai Takeda's seal, for example, is an Oriental Dragon). However the kaō continues to be widely used, and sometimes the seal was used in addition to a kaō. Also note here that not all seals were/are hakubun (red background stamp where the unstamped white areas form the words). I would even say hakubun would not have been the majority, or at least not a clear majority.
The 血判状 keppanshō, literately "blood-seal-edict", are documents only used in really official agreements, like an alliance or something. The blood-seal is to signify how strong the pledge or alliance or allegiance is. And yes, it's done by cutting one's finger and stamping in blood on/beside one's kaō.
In terms on commonality in the Sengoku, kaō was definitely the most common.
