cv.vocabulary_ in this instance is a dict, where the keys are the words (features) that you’ve found and the values are indices, which is why they’re 0, 1, 2, 3. It’s just bad luck that it looked similar to your counts 🙂
You need to work with the cv_fit object to get the counts
from sklearn.feature_extraction.text import CountVectorizer
texts = ["dog cat fish", "dog cat cat", "fish bird", "bird"]
cv = CountVectorizer()
cv_fit = cv.fit_transform(texts)
print(cv.get_feature_names())
print(cv_fit.toarray())
# ["bird", "cat", "dog", "fish"]
# [[0 1 1 1]
# [0 2 1 0]
# [1 0 0 1]
# [1 0 0 0]]
Each row in the array is one of your original documents (strings), each column is a feature (word), and the element is the count for that particular word and document. You can see that if you sum each column you’ll get the correct number
print(cv_fit.toarray().sum(axis=0))
# [2 3 2 2]
Honestly though, I’d suggest using collections.Counter or something from NLTK, unless you have some specific reason to use scikit-learn, as it’ll be simpler.