BTW..the first scale degree is considered the tonic
2nd scale degree is "supertonic"
3rd scale degree is "mediant"
4th scale degree is "subdominant"
5th scale degree is "dominant"
6th scale degree is "submediant"...can be also called "superdominant"
7th scale degree is just called "leading tone"
The dominant chord doesn't always have to be on the dominant scale degree either. That is what secondary dominants are, basically, a 7th chord that is used as a moulation into another key. A figured bass example might be a V/V chord. In the key of C Major, that would be a 7th chord based on the second scale degree of C Major, D-F#-A-C. In case nobody really knew what they were....
I think I might just say all this a little vague for more question/answer. 7th chords are the most abundant of all chords. They have a shit load of names and uses, and some don't even have names. To put it fundamentally, to be a 7th chord, the triad just adds a 7th above the root of the chord. And then of course, it is no longer a triad.
A Dominant 7th chord is basically a Major triad with a 7th that is a minor 7th above the root note of the chord. A C dominant chord is spelled as: C-E-G-Bb. That Bb is what makes it a dominant chord.
A Major 7th chord is basically a Major triad with a Major 7th above the root chord note. A C M7 chord is spelled as: C-E-G-B. That C to B natural is a Major 7th.
The minor 7th chord is C-Eb-G-Bb. It's just a minor triad with a minor 7th. There is also a "minor Major 7th chord." It is just a minor triad with a Major 7th above the root note.
Then there is either a fully diminished 7th chord or a half diminished 7th chord. A fully diminished 7th chord is just a stack of minor thirds, basically, a dim triad with a dim 7th. A Cº7 (the º means fully dim) chord is: C-Eb-Gb-Bbb. A half dim 7th chord is C-Eb-Gb-Bb. That's a dim triad with a minor 7th. For a half dim chord, the "º" would have a slash through it.
These were all pretty "normal" 7ths chords though, there are different ways to use them in modulations.
A Neapolitan chord is one example of this. Usually in the minor keys, it is a Major triad based on the b2 scale degree, or bii. So in the key of C major, the Neapolitan chord would be Db-F-Ab. (In the minor key, the supertonic triad is a dim triad.) This chord has no roman numeral, it is just "N." But, it is most likely to be found as a first inversion, so it's really "N6."
The last one I'll tell of are the aug. 6th chords.
There are three types of aug. 6th chords: French, German, and Italian.
All augmented 6th chords have a sharp 4 and an aug. 6.
The basic augmented 6th chord is almost always based on the b6 scale degree or minor 6 scale degree. In the key of C major, it will be Ab.
And each of the three types have a different set-up. The Italian aug. 6th chord in the key of C major is: Ab-D-F#-Ab. It has an aug. 6th above the root, a double of the root, and an aug. 4th. The French aug. 6th chord in the key of C major is: Ab-Bb-D-F#. Instead of the doubled note, it contains a Major second above the Ab. The German aug. 6th chord is like the French except that instead of a Major second it's a minor third, Ab-B-D-F#. The German aug. 6th chord almost looks like a mispelled Dominant chord, except the fact that the Ger. aug 6th chord resolves very differently. And like the N6 chord, these aug 6th chords have no roman numeral. They are labeled as: Fr.+6, Ger.+6, and It+6.
There are tons of other 7ths chords, but it would be almost pointless for one to write them all down.