If I don't err, in the literature a stream cipher is one in which each plaintext bit is processed individually, commonly via xor-ing with one bit of a random or pseudo-random bit stream, while a block cipher (in ECB mode, i.e. ignoring the add-on processing operations like CBC etc.) operates on n bits at a time with operations that are the same for a given key, i.e. each successive groups of n bits are processed in exactly the same manner.
If one looks at the corresponding literatures, one finds in the first case mostly works on linear or non-linear feedback shift registers and in the second case ideas of design of a rather different genre. That could justify the differentiation in terminolgy however IMHO only on the assumption that no cipher designs could lie inbetween the two categories. But that assumption seems to me to be an invalid one. Anyway, let's consider the classical ciphers. Is a Vigenere cipher or a (additive) cipher with a running key a stream cipher or a block cipher? That question seems not to be very satisfactorily to be answered, I am afraid.