This depends on what navigation software you're using, but I have some experience editing the Waze map. The way it works on Waze is that your phone sends the server your desired start and end points, and the server responds with a list of all the intersections you need to traverse in order. (This is actually a series of road segment junctions, wherever the map editors joined two road pieces together). These intersections can contain metadata on how to announce specific turns, but generally don't because there's an algorithm that looks at the angle the segments meet at and automatically decides how to describe the turn. The places I've seen it manually overridden include intersections where two divided highways meet at an angle far enough from 90° that it gets confused about how to announce a left vs a u-turn. I've also seen forks in the road where the side road requires less of a turn than continuing on the main road and the algorithm gives ambiguous instructions, like "continue straight" meaning turn onto the side road.

Edit: On your point about non-visually noticeable "blips". This is also pretty common when roads change width right at an intersection (e.g. adding turn lanes). The Waze map doesn't include road width in its data, so editors usually draw it down the centerline of the road. If the road changes width suddenly, you have to choose between keeping the line straight-ish, or faithfully following the centerline, which can mean that if you were to zoom way in there can be weird jumps and sharp angles that get smoothed out by the visual renderer

My Spanish is mediocre, but typically can get me from A to B without a lot of misunderstandings. I was driving back from the Mall in San Juan, Puerto Rico, and my very British GPS decided to route me via "Calle Ajore." Now everybody uses abbreviations for the word "street" - and in Spanish uses "C." For "Calle" just like English uses "St."

So, I'm battling traffic, and Lady Winifred Windsor the GPS advises me to "Turn right to see a whore."

It doesn't have to analyze the map visually, the graphical map you see on your screen is the part that's generated locally by your device. The map data your device receives is already in vector form, which is a mathematical list of angles, line lengths etc.

I think it's analyzing the angles between the curves dynamically, with manual overrides in some places where they have been added. I don't think this would be very computationally expensive to do on the client side, but it could be cached as metadata.

I imagine it's done by hand and your experience with the mistake was just that.

I remember the early days of this tech where the program controlling the voice output didn't know how to distinguish between "Dr.", the abbreviation for doctor, and "dr", the abbreviation for drive. So it would tell you to turn onto Doctor Martin Luther King Doctor and other wacky things.

Mine likes to say "turn slightly left" for small bends and "keep left" for lanes.