In order to understand chords and scales and how they are structured, you need to understand what an interval is. Quite simply an interval is the distance between any two notes.
Semitones are also known as Half Tones in the US, which is really the same thing as the word semi literally means half. Semitones are the smallest possible interval in western music ( some other cultures have smaller intervals), so therefore it is two notes right next to each other on the piano (this includes the black notes as well as the white notes). Examples of semitones include B to C, F to F sharp and B flat to B.
Tones are also known as Whole Tones in the US, so again they are basically the same thing, just the US term has the extra adjective. Tones are quite literally two semitones, so they have one note in between and yes you need to take into consideration the black notes when you are working them out. Examples of tones include C to D, E to F sharp, C sharp to D sharp and B flat to C.
There are also other intervals known as a 2nd, 3rd, 4th, 5th, 6th, 7th and 8th. The way to work these out is by counting the note you start on, the note you finish on and all the notes in between. When I first learned this as a kid, I would often get it wrong because working out intervals is not the same as working out addition in mathematics. In Mathematics, you start counting after the first number, not including the first number. As soon as I got my head around this important distinction, I found working out intervals easy.
Intervals not only have a distance (number) but they have a quality too. When working out intervals, you must always work out the distance part before the quality part.
Intervals that are a 2nd, 3rd, 6th or 7th are called major intervals when they are found in the major scale of the lower note. If the top note is a semitone lower (so that the interval is a semitone smaller than the major interval) it is known as a minor interval. If it is a further semitone lower than the minor interval then it is known as a diminished (dim) interval. If the top note is a semitone higher than the major interval then it is known as an augmented (aug) interval.
If the intervals are of a 4th, 5th or an 8th and are found in the major scale of the lower note, they are known as perfect (perf). The terms major and minor are never used to describe 4ths, 5ths or 8ths. If it is a semitone lower from the perfect interval then it is called diminished and if it is a semitone higher than the perfect interval then it is known as an augmented interval.
When trying to work out the quality of an interval, after you have worked out the distance, ask yourself whether the top note is found in the major scale of the bottom note and then work from there.
It is also possible to get intervals of a 9th, 10th, 11th, 12th, 13th and 14th but these are really just smaller intervals, with an octave (8th) further apart so:
A 9th is the same as a 2nd,
A 10th is the same as a 3rd,
An 11th is the same as a 4th,
A 12th is the same as a 5th,
A 13th is the same as a 6th and
A 14th is the same as a 7th.
I hope you now realize how fundamental it is to know about intervals, because it really is the key to understanding how chords are built.