Terminology: Is a block cipher in counter mode still considered a block cipher or is it classified as a stream cipher? I'm confused about what terminology to use. I see people referring to such a cipher-MOO combination using both terms.
A block cipher is a block cipher. But if it is used within counter mode it becomes a block cipher within a streaming mode of operation. The resulting cipher has the external properties of a stream cipher. The block cipher now acts as a stream cipher. But I would not call it a stream cipher, because that would probably fool readers that the cipher has the internal design properties of a stream cipher.

In other words, streaming modes such as CTR simulate a stream cipher, but it doesn't emulate it. Externally it does show it to have certain properties, but it is does not try to be one internally. For instance, the key remains protected by the block cipher, rather than by properties of CTR which defines how to perform the streaming.

For these reasons I would prefer a sentence like "using CTR mode lets you use a block cipher as a stream cipher" rather than "using CTR mode turns the block cipher into a stream cipher". You could use the term "stream cipher" after such a clarification, I suppose, in case you don't want to get stuck with "block cipher in stream mode of operation" which may be too large / descriptive in texts.