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Stemming removes suffixes and the result is not necessarily a word. Lemmatization gives the word from it's derived. Spacy doesn't even have stemming as the creator doesn't consider it useful.
Bag of words (BoW) is quite old, word2vec is oldish (2013), but they can still perform well enough, depending on what you want to do. FastText is also "old" (2016), even though it's a very good baseline and it's actually kinda based on a bag of words model and the skipgram model that was introduced with the word2vec paper. The hot new thing is HuggingFace and the BERT family of models, but they are orders of magnitude more resource intensive.