Almost all random number generators, whether software or hardware, end up producing blocks of bits. For software, this is because it is wildly inefficient to produce single bits, and so algorithms generally produce large numbers of bits at once.
For hardware, this is because the hardware used is often imperfect and may have a slight bias, or it could end up being broken altogether and descend into either a large bias or just a single output. As a result, a hardware RNG will contain code to process blocks of bits, perform statistical tests on them to determine if they are likely to be the result of a large bias or a malfunction, and if they pass the tests, run them through some sort of conditioning algorithm which condenses a large number of bits into a smaller number of less biased bits. This can be done using something like AES with CBC mode, a hash function, or simpler approaches, like Von Neumann debiasing.
In any event, using any sort of RNG to generate a symmetric key like for AES-256, the bits or bytes are produced by the RNG, and then the proper amount (in this case, 256 bits or 32 bytes) are taken and used for the key. It really doesn't matter whether we prefer to write the RNG output or the key as individual bits, as bytes, or as larger numbers, provided we agree on the bit and byte ordering to be used. Thus, the word "number" is only used in the most generic sense as meaning some integral quality in some base we'd like to use.
Another term for a cryptographically secure pseudorandom number generator (CSPRNG) is a DRBG (a deterministic random bit generator). The latter is less commonly used, but it is notably used for several designs specified by NIST. In fact, the CTR DRBG is used in Intel chips for the RDRAND and RDSEED instructions. A hardware RNG is used to generate a set of bits, which are then tested and debiased, and those bits are then used to seed a CTR DRBG instance in hardware. But either way, the two terms are mostly equivalent.
