I have found myself doing both but not sure which is the right way. Sometimes I see a note then I can see the next note is a 4th above it so I play it but I actually don't know what note I just played if that makes sense. I only know it was a 4th up from the last note. Is this wrong?
We get to a point where we do NOT look at a dot, think 'that's a D', then find it on the instrument. And it could be any instrument.
We often see how many lines or spaces (or combinations thereof) separate notes, and play accordingly.
Sometimes we even second guess where we think the tune may go, and stab at that note.
There are many tricks we use, and intervals is one of them.
EDIT: just to add that having the scale notes of the key on high alert makes life that little bit easier - partially because when accidentals occur, it's clear that those notes will be among the five we've avoided - until now!
I don't think this is wrong at all; my sight reading is a mixture of these components, as well.
The fact is that part of sight reading is based on common patterns. This is one of the many reasons why we work on scales and arpeggios and the like: when we encounter them while sight reading, we can call upon that ingrained memory to easily perform the task.
And some of these common patterns are interval based, which allows us to sight read larger portions of music without knowing every single note that's being played. Seems perfectly fine to me!
Perhaps both are good, and there are other options. How one reads is instrument dependent. On the guitar for example we eventually learn to read chords. This can pose a problem for beginners as they feel like they need to stop at the chord and climb up it, reading each note one by one and finding it. In fact this is not a good way to read chords. One is much better off identifying the intervals and then grabbing the them with the hand. Good guitar books teach one how to identify the chord shape (what the hand needs to do to get the chord in standard tuning) with the stack of dots on the sheet music. If taught correctly, and practiced, one can learn to read chords on SMN with no problem.
Sometimes I look for geometric shapes in the music and relate them to scales arpeggios and intervalic leaps. My hand knows what to do. This also makes transposition on the fly easier. There is no need to force yourself to read by note name identification.
There is a big gap from a beginner's sight-reading to an experienced musician's sight-reading.
Sight-reading consists of reading the notes, the intervals, rhythm patterns, scale patterns, chords patterns, broken chord patterns, key signatures, tempo indications, articulations, dynamics and any other indications that might appear in the sheet music.
The beginner reads one note at a time, a skilled sight-reader reads many notes at the same time as well as the relation between the notes, and that relation is composed of intervals and all those patterns mentioned above.
A good sight reader can read a whole bar with just one glance at the bar, well dependning on how complicated the bar is of course. Some bars need a close look at details, others are simple and easy to read.
There can be differences on how you read depending on which instrument you play. I play both the violin and piano myself and the sight reading are different on those two instruments although the points I wrote above are valid for both of them. But the way you read is related to the instrument you play in that you relate the notes to the instrument. You see a note and immediatly think of that particular place on the instrument. This means that despite that playing technique is a different subject you do relate what you read to the playing technique. You are of course concerned about how to play it.
Here are some examples:
This is not wrong, and it may be individually better for a singer or violinist.
Identifying the notes, realizing their position in the staff, their function in the scale, their value, position and function in the chords, recognizing motifs, Melodic patterns, sequences, keys ... everything is helpful, useful, everything makes sense, also the interval to the previous note, but this latter is the less important to me, only regarding other aspects like solfege and harmony.
On the piano:
In chordal passages I think it's the shapes of the chords I take in. Like which inversion. If the note-heads are all on the same side of the stem it's going to be a simple chord. If one of the note-heads is on a different side from the others, its position on the stem tells me it's going to be this type of chord, or this type.
In fast passages where the hands are jumping between registers and I can't afford to take my eyes off the music, I think my fingers slightly trail along the black note groups to find the right location. Sounds ridiculous when I describe it, but I think a slowed-down film would show that.
With runs of notes I think I think(!): 'Looks like a scale. Yes, with an accidental. Where does it end up?'
Then, 'Here comes another one. Looks like the same length.'
As Tim said, it often involves guessing. 'It's likely to be this'.
In easy passages I think I glance ahead at any difficult bits coming up.
My recommendation is to read as many notes as possible and practice it this way if you are beginner specifically. You can get away reading a few intervals but if one is wrong the others automatically become wrong, so avoid it as much as possible.
In short: Read the notes, read the intervals to get by only.
With experience, and when a piece lies within your comfort zone, you read the patterns. Like 'look and say' in reading a book. When an unfamiliar pattern presents itself, you may have to stop and look at it in a more analytical way.
There's another stage, particularly when playing non-classical (for want of a better term) music like a song copy or a lead sheet, where you just read the music. Easier to do than to describe! You take in what the music DOES rather than the specific notation, and you play something appropriate.
There can be a danger of doing this too much. Sometimes I have to pull myself back with 'Hey, this looks like quite a neat piano part! Perhaps I should try playing what it SAYS...'