Fretboard Diagram
A freeboard diagram is essentially a drawing of the fretboard. Six horizontal lines represent the six strings. And a number of vertical lines represent the frets. We will find it usually on a horizontal position where the first string is the upper line (as in tablature). 
The little number you see beneath the diagram ar position indicators to help us navegate the diagram more easily. We can add as many indicators to a diagram as we want or need. The most common to find are 5, 7 and 12.
Sometimes we’ll find the fretboard incomplete. 
Other times we’ll find just a section of it. In such cases, we use numbers outside the fretboard to show what frets are being represented. 
What do we use the fretboard diagram for?
Just as we can use a geographical map to notate different things (like the location of rivers and lakes, or the demografics, ets), so the fretboard diagram can be used to map different aspects of music.
For the purpose of this introduction to the fretboard diagram, we will see examples of one showing the location of the natural notes. (Which is a super important thing to know and memorize). 
Fretboard diagram and chord diagram
The visual aspect of the fretboard diagram is similar to the chord diagram, but its usage is different in most cases. The fretboard diagram is mostly used to show the locations of notes, but we are not intended to play them all at once. It is meant for us to know where to find a group of notes.
On the other hand, in regards to the notes that a chord diagram, we are meant to play all of the notes that the diagram shows.
In fact, the tw diagrams sown above, can be connected. We can see the first diagram as some kind of “menu” from which we can select notes to create chrods. And the second diagram shows a selection of those notes. This selection happens to create a C major chord.
I hope this has been helpful.
Happy practice! 🙂