What is different about a carboxyl group and an amino group?

A carboxyl group (-COOH) functions as an organic acid (deprotonate to -COO^-). An amino group (-NH₂) may function as an organic base (protonated to -NH₃⁺). Therefore an organic compound that has a carboxyl group is likely to have an acidic pH and an organic compound with an amino group is likely to have a basic pH (precise degree of acidity and basicity depends on the number of carbons in th backbone, the number of carboxyl or amino groups, and the presence of other functional groups).
Some molecules that have both carboxyl groups and amino groups (amino acids, for example) can function as either an acid or a base under different circumstances, making them useful in buffering the pH of solutions.