Is there a difference in sound between standard tuning and Drop C if I play the same notes on both? For example, C and D on 8 and 10 frets in standard tuning on the first string and the same notes on 10 and 12 frets in Drop C. If I understand correctly, problems may arise only on the first two frets (and on the first four in the case of the sixth string). Am I right?
There certainly can be a difference in the sound when you play in drop tunings on an electric guitar. The primary factor is the tension that the strings expect to be played at. As you tune down lower and lower, there is less and less tension in the strings. Things can start to get sloppy, notes don't sustain as long, and there can be other issues that arise as well.
One way to combat the sloppiness in a drop tuning is to use a larger gauge string than what originally was in place. I have an acoustic guitar which I keep tuned to C-Standard (C-F-A#-D#-G-C) which uses Elixir medium strings, which are .013-.056 gauge. Those heavier strings compliment the dropped tuning nicely, and I would never try to take that guitar up to E standard tuning.
I experimented with Major Thirds tuning on an 8-string electric guitar with a 27" scale length for a while. In order to get the right tension out of all the strings, I mixed and matched strings from two different flatwound guitar sets, and also used a flatwound bass string for the low E on that guitar. That required a bit of modification to the string hole in the low E tuning peg.
Bottom line is, if you tune down and you can't hear or feel a difference in the notes being played, then everything is fine. If you notice things not sustaining or feeling sloppy, you may want to look at using larger gauge strings to offset that.
Going a bit off your specific question, For an electric guitar, 99% of the sound quality is defined by the pedals, stompboxes, filters, preamps, etc. in use. The drop tuning won't matter.
By comparison, for an acoustic instrument, changing the fundamental (open string) pitch changes the inter-string resonance relationships. The overall sound will be different. Two examples:
-- Here and there (Mahler, e.g.) composers use raised tuning on one violin string to make the sound more strident or macabre.
-- Bach's 5th Cello Suite was originally written with the A-string dropped to G. The sound is noticeably warmer on G-harmonic notes.
A drop tuning is going to reduce the tension on the detuned string. This will primarily affect a few things:
- Intonation; applying the same amount of pressure to the string with your fretting hand will bring you more and more sharp as pressure increases
- Action; the action will be lower and this can cause buzzing if you aren't set up properly for the drop tuning
- Attack; the sound of your attack (when you strike the string with your pick) is going to change as string tension changes in general