What's the difference between word-oriented and byte-oriented ciphers? I am currently learning about the RC4 cipher and its improved version called Spritz.

The paper of Spritz says 


  We do not consider other stream-cipher proposals here, and expect that for many applications other word-oriented architectures may be a better choice than the byte-oriented RC4/Spritz style.


Now, what I don't quite understand:


What's the difference between a word-oriented and a byte-oriented cipher/algorithm?
When should either a word- or byte-oriented cipher be used, and
What are the advantages/disadvantages of each?




I found some papers that introduce a byte- or word-oriented cipher, but without elaborating clearly what's the idea behind it. To my surprise, googling for "word oriented byte oriented" and checking several Wikipedia pages on computer architecture/CPUs didn't really yield useful results to me.
To my understanding the only difference between word oriented and byte oriented is that word length depends on the processor used, so maybe 32 bits or 64 bits long, for example.

The idea of a word oriented cipher is that it uses native operations to hardware, processing words instead of bits, making for higher speeds, but clearly that makes designs technology dependent which may not always be the best way to go. Mixing addition mod $2^{16}$ with $GF(2)^{16}$ and multiplication mod $2^{16}+1$
can be complex to analyze. Thus word oriented operations have a complex algebraic representation which may be considered a plus for the designer, but then reliable analysis of such operations also hampers the designer.