There are 3 different ways of Guitar-chord notation and reading:
staff of 5 lines like almost all other instruments
Chord-TAB (as you are showing here) they are used for finger picking and more differentiated accompaniments e.g. bass licks.
Chord diagram: mostly used for lyrics and added chords - what you're calling "words"
(from the chord-diagrams (patterns) you can also play a differentiated accompaniment when you have some experience of finger picking or bass passing notes.)
Why are there words that appear on guitar tabs?
As you know the chord TAB shows the 6 strings and the numbers indicate in which fret they are "hold" by the fingers of the left hand.
The terms C, Am Fmaj7 etc. are the names of the guitar-chords that are played in the chord TAB and the chord diagrams are just another representation of what we are doing when we want to play a chord:
The strings are shown vertically, the chord-names ("words") are written on the top and at the bottom are notated the fingers that have to work on the specific strings.
If you turn one of these patterns 90° to the left you will recognize that they're resembling to what you have learnt by reading the chord-TAB. But instead of the numbers the diagram shows where (in which fret) you have to put your fingers and the numbers on the right side of the rotated diagram indicate which finger you must use.)
So the example of Am means a-minor (A-C-E) shows we have from string 6 to 1:
D (2nd fret= E) -> finger 2
G (2nd fret= A) -> finger 3
B (1st fret= C) -> finger 1
You will recognice the similarity with the 2nd chord named Am in your TAB: notice that the bass tones are not played there.
Now you should be able to derive all the other chords and write your self the corresponding TABs from the chord diagrams and vice versa.
Edit: I think the fingering of A major (2nd diagram) has a typo. I've never seen A = 213! we better use 123. That's why I poste another list of diagrams where you can compare also "your" Fmaj7. It is exactly like Tim has described.
You'll find 100reds of lists looking up: Guitar chords (images).