Difference in Basic Amino Structures
Your description is more or less correct, but so are both images. The bottom images shows the predominant form the amino acid would take at neutral pH (or any pH between ~2 and ~9.5). This is because the caroboxylic acid (-COOH) and amino (-NH2) groups are a weak acid and base and can lose or gain a proton (hydrogen cation), respectively. pH below the pKa of the functional group (~2 for carboxylic acid and ~9.5 for amino) favours protonation whereas pH above the pKa favours deprotonation. Also note that the "centre carbon" (the α-carbon) did not gain a proton in the second image, it's just drawn differently.

You could try this website for an overview of acid/base chemistry and perhaps these Wikipedia sections on zwitterions and isoelectric points with respect to amino acids, though there are many alternative sources of material available if you search for them. This question and answer may also be useful for you, at least eventually.