Case folding is mapping everything to lower case. Whether applying it depends on the tasks. In information retrieval or speech recognition, it is very helpful. However, for sentiment analysis and other text classification tasks, information extraction, and machine translation, keeping cases can help differentiate words. For example, US the country and us the pronoun.

University of Michigan - Ann Arbor

Word normalization is the task of unifying words/tokens to a single standard format. The methods below are widely used depending on the tasks.

- Case folding
- Lemmatization
- Stemming

Word normalization

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

Stemming a simpler but cruder alternative to the lemmatization, which mainly chops off word-final affixes. The Porter Stemmer is the most widely used stemming algorithms.

Stemming

Case folding

Lemmatization is to determine that if two words have the same root, despite their surface differences. For example, $am$, $are$, and $is$ have the shared lemma $be$; the words $cat$ and $cats$ both have the lemma $cat$.

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