These are the two types of verbal magic frequently used in this AU. Spells can't be cast by just anyone; those with the magical ability to spellcast are the only ones who can read a spell and actually make something happen. The Pines have a rich history of powerful female spellcasters, such as Pippa, but Pacifica is the first girl in the history of the family to be completely unable to cast a single one, which is why she collects magical objects and jewelry instead. On the other hand, Dipper is the first Northwest to ever have spellcasting abilities. (It's also implied that male spellcasters are very rare, so congrats to Dipper.) However, he is not aware of his ability until he accidentally cast a spell summoning zombies with a spell from Pacifica's grandmother's diary while trying to convince her that magic isn't real. That plan kind of backfired on him.
Wordsmithing is the ability to use normal speech and conversation to magically influence whoever they're talking to/whoever hears them into doing or thinking something. Certain phrases and significant words can be used to make a wordsmith spell even stronger, such as 'please' or any other word/phrase that the wordsmither focuses their power on. Usually, it takes a lot of concentration and focus to wordsmith, but in some cases like Dipper's, one's ability is so powerful that they could do simple wordsmithing without even realizing it.
It's unclear how Dipper developed his spellcasting and wordsmithing powers, especially since the Northwest don't have a history with it like the Pines do. It's possible that his powers could be a side-effect of Bill's presence in Mabel since their birth; a part of his powers could have leaked into Dipper while entering Mabel and shaped into spellcasting and wordsmithing powers.
A side note, rituals and summonings can be performed by anyone, provided that they follow the instructions correctly.