If you are using these words as they apply in genetics, then it is both.
An amino acid is specified by a codon of three DNA letters, and there are four choices for each letter slot - namely C, G, A and T. You can think of a codon as a word; in the DNA language words are only made up of three letters.
How many different words can DNA express, theoretically? For each letter there are four options, so the maximum number of words must be 43 = 64.
However, DNA only uses 21 words (or 23, depending on how you count). 20 of these code for amino acids, and there is also a stop codon, which tells the cell's machinery when the protein ends. (Actually, there are 3 stop codons, but these have identical 'meanings' to the cell, and are therefore best counted as one.)
The fact that DNA could accommodate a larger variety of meanings (namely, 64) than it does (namely, 21) means that, in a technical sense, the DNA code is degenerate.
The redundancy of the DNA code refers to the fact that either strand of the double-stranded DNA is theoretically enough to specify all the information in the genome. This is true because the two strands simply mirror one another - they're complementary.
If the other strand doesn't technically hold any additional information, why does the body persist with it? Chiefly, the complementary strand is useful to the check for, and correct, errors. (Having two copies of an important document is vastly preferably to having only one. If you spill coffee on one copy and can't make out some of the words, you can use the remaining copy to fill in the gaps.) There are probably also additional reasons for having two strands, such as keeping the information-carrying nitrogenous bases safely tucked away on the inside of the DNA molecule.