Tuning is a comparison, not a measurement. The tuner finds the fundamental of what it hears, names the nearest note, and reports the gap in cents so you know which way to turn the peg.
Cents, not hertz
A hertz means something different at each end of the instrument. Three hertz sharp on a low E at 82 Hz is 63 cents, most of a semitone. Three hertz sharp on the top E at 330 Hz is 16 cents, which is close enough that many players would not hear it in a chord.
Cents fix that. One cent is a hundredth of a semitone at every pitch, so the same number on the meter means the same audible error whichever string is ringing.
Choosing the instrument
The preset does two things. It draws the string targets, and it tells the detector which frequencies to search.
That second job matters more than it looks. Wound low strings put a lot of energy into the second harmonic, and a detector searching from 27 Hz upward will sometimes lock onto it and report a note an octave high. A guitar preset searches from 68 Hz to 527 Hz, so the octave error has nowhere to go.
Chromatic mode searches 27.5 Hz to 2.1 kHz, which covers a 5-string bass low B up to the top of a violin. Use it for anything without a preset: a wind instrument, a singer, a synth patch you need to match.
Response
Response is how hard the needle is damped, and the right setting depends on the string.
A low B on a 5-string bass is 30.9 Hz, one cycle every 32 ms. The detector needs several cycles before a reading exists at all, and a fast needle on top of that reads as jitter. Steady is the setting for the bottom of a bass. Fast is better on a ukulele, where the note decays before a slow filter has settled.
The needle also ignores its own smoothing when the pitch jumps more than a semitone, so moving to the next string snaps rather than sliding across the gap.
Concert pitch
The reference is A4, and every other target is derived from it by equal temperament. Moving it to 432 Hz or 415 Hz moves all six string targets together.
Early music is the usual reason. A415 is roughly a semitone below modern pitch and is the common baroque standard, so a modern instrument playing with a period ensemble is retuned rather than transposed.
Where the reading gets unreliable
The detector reports one fundamental at a time. Strum a chord and it reports the pitch the notes divide into, which is usually not any of them.
It also needs a periodic signal. A muted string, a note plucked and immediately damped, or a room with a fan running gives a low clarity figure, and cents readings below about 70% clarity should be treated as a rough guide rather than a measurement.
Microphone tuning has one limit no software fixes: on a loud stage the microphone hears the band, not your string. A clip-on tuner reads the body of the instrument instead, which is why they exist.