Many charts will show that they are using data from surveys over 100 years ago. In practice surveys from 100 years ago and built up through triangulation are often very accurate in terms of the relative position of one thing compared to another. So if there was a survey of a remote island, the position of different visual landmarks making up the island with respect to each other, will generally be very accurate.
The challenge is that all of these sets of measurements require some sort of starting point to begin measuring from, e.g. an initial datum. While measurements taken via triangulation may well be accurate to a few metres, the initial datum, e.g. the position of the island itself may have been taken based on star positions and could easily vary by half a mile.
Because of this it's important when comparing charts and electronic devices to ensure they have been explicitly set to use the same datum.
While this is less of a problem in the age of GPS, a problem it still is due to the earth not being a perfectly uniform shape. More on the current standard (WGS84) here: https://en.wikipedia.org/wiki/World_Geodetic_System.