What's the difference between word-oriented and byte-oriented ciphers?
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.