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I am learning how to build chords.

As I understand the 13th chord contains 1, 3, 5, 7, 9, 11, 13 interval.

For Cmaj13 for example its gonna be C, E, G, B, D, F, A notes.

I see many 13th chord shapes on internet but how does that happen?

Guitar has only 6 strings, so how do I press 7 notes at once?

If I skip any note, its gonna make it another chord, so how to do that?

Please help me understand, thank you

"If I skip any note, its gonna make it another chord..."

No. First: despite the 'pile of 3rds' method of constructing chords in our textbooks, in a 13th chord the 5th may be omitted, the 9th is often omitted and the 11th is ALWAYS omitted. (OK, ALWAYS is just asking for people to come up with exceptions. But it's near enough, and we're talking about the 11th, not a ♯11)

Second: On guitar - and any other instrument that can play chords - it's common to outline chords rather than play every note. In context, the 3rd, 7th and 13th may be all you need, particularly in a band where the bass player has the root. We don't actually strum full 6-string chords all that much!

Leaving out a note may leave room for ambiguity. If we play G13 without the D, it allows the possibility of it actually being G13(+5). But that's OK.

Let me first show you the most common (and good sounding) voicings of 13th chords on the guitar. I take as an example a C13 (from low E to high e):

8 X 8 9 10 10 (chord tones: 1, b7, 3, 13, 9)

8 X 8 7 5 5 (chord tones: 1, b7, 9, 3, 13)

X 3 2 3 3 5 (chord tones: 1, 3, b7, 9, 13)

They all have five notes (instead of seven) because you always leave out the 11 if you have a major triad as a base chord. The 11 clashes with the third because it is a minor ninth above it (or a minor second, depending on the voicing). You can't say that the 11 is not allowed because anything in music is allowed, but if you see a C13 chord in a chart, I can guarantee you that nobody in their right mind plays the 11. Usually, you would also skip the 5th, because the 5th doesn't add any color, and it makes the chord just sound very dense. So the really relevant notes are: 1, 3, 7, 9, 13. And even here you can prune a bit. If you want to play a 13th chord, of course there should be the 13, but you don't necessarily need the 9; it's just an optional color. You do need the 7th to make it clear if it's a dominant seventh chord or a major seventh chord, and you do need the 3rd because otherwise you don't hear if it's major or minor. You do not always need the root in a guitar voicing. The root can be played by the bassist or the pianist, or it can be implied by the context. So the absolutely necessary notes for a 13 chord that you really shouldn't leave out are (in my humble opinion): 3, 7, 13.

In any chord, the root is the most important. Without that, the chord has no name!

Next comes the third, defining either major or minor. The fifth is often omitted, as its sound can be heard in the second harmonic of the root.

Then onto the 7th. Important again, as there are three different 7th notes, each blending with the others to make the sound of the chord.

So far so good, on guitar. Next is the 9th, which is often major 9, but can also be ♭9 or ♯9. the 11th can clash with the third, so care is taken there. The 13th is an octave copy of the 6th, an is not really going to clash.

Playing a 13th chord doesn't mean - especially on guitar - that all the lower notes need to be played, so 11 and 9 can be left out. Best is to list all the notes - 1,3,5,7,9,11,13, nd try to find a combination that sounds good (and is playable!) for you. If there's a bass playing, the root can go too.

On guitar, my go-to shape is 554577 (for D13). There's no 9 or 11, and it's in 2nd inversion. Basically, it has the 7th (b7) and M6. Maths: 7+6=13!

When we play chords with that many notes we have no choice but to drop a few. This occurs in music theory too. It is a common practice to drop the 5th from a dominant 7th chord, and double the root, for example C7 played as C, E, Bb, C. This is often played on guitar in the first position as (x, 3, 2, 3, 1, x). I'm assuming my notation is self explanatory and x means don't play that string. Again, I stress that this voicing is recommended in classical music harmony texts and not to accommodate any specific instrument.

The movement C, E, Bb --> C, F, A sounds very nice and the 5th of C7, G, doesn't really move gracefully to a note in the F chord (though one can move it to F or A or even leave it resolving C7 --> Fadd9). But I digress.

As for the 13th I'm going to describe it in terms of the dominant 13th rather than the Maj13 as you have stated, but the comments do apply in general.

Since we don't have enough strings or fingers to play the whole 13th chord a common practice for playing 11th and 13th chords is to simply add the 11th or the 13th to a dominant 7th chord, ignoring the 9th and 11th (in the case of the 13th). A common voicing of the 13th on guitar is

F13 = (1, 3, 1, 2, 3, 1) = (root, 5th, b7th, 3rd, 13th (or 6th), root).

Another common voicing that follows the form of "fat chords" with a large interval in the bass is

F13 = (1, x, 1, 2, 3, x) = (root, x, b7th, 3rd, 13th, x).

And it is sometimes common to include the 9th as in

C13 = (x, 3, 2, 3, 3, 5) = (x, root, 3rd, b7th, 9th, 13th)

When I first learned these my guitar teacher said just grab the notes you can. This gets the chord forms in your muscle memory. After learning more about music theory and harmony I would say that the choice of form should be such that movement into and out of the 13th is graceful, that is you hear close movement of the notes, resolution, etc.

In closing the thing that makes the 13th a 13th is the dominant 7th foundation with the 6th added. I'd extend this to the Maj13, i.e. Maj7th with the 6th added. You want to hear that 7th degree or it's just a 6th chord or an add6 rather than a true 13th. The fingerings I've provided can be extended to Maj13 by raising the b7. You can free up fingers by dropping the 5th (which can be done on extended Maj chords as with Dom 7ths). The key to choosing a voicing is in how it moves to the other chords.

Others have given good answers, but I'll add one more perspective. 13th and 9th chords are good examples of chords where a guitarist can easily omit the root note, and nobody will notice, if you just don't play any very low notes. Or at least that's my own experience. If there's a harmonic progression that provides enough context to make the listener guess what should come next, it feels as if even the tritone Bb-E alone said "C" or "C7". The 13th and/or 9th notes just add more detail and credibility to the story.

Here's an example 12-bar blues in C, where root notes are not played, but I think it can perfectly legitimately be said that the chord symbols C13, F9 etc. are being played. You could add a bass line to this, and it would make it sound fuller, but IMO the harmony is complete even like this.

The piano solo in the second verse tries to avoid playing root notes as well.