I found Sentiment Analysis and Emotion Recognition as two different categories on paperswithcode.com. Should both be the same as my understanding? If not what's the difference?
Sentiment in this context refers to evaluations, typically positive/negative/neutral. Sentiment Analysis can be applied to product reviews, to identify if the reviewer liked the product or not. This has (in principle) got nothing to do with emotions as such.
Emotion recognition would typically work on conversational data (eg from conversations with chatbots), and it would attempt to recognise the emotional state of the user -- angy/happy/sad/...
Of course the same can overlap: if the user is happy, they will typically express positive sentiments on something.
Also: emotion recognition goes beyond text (eg facial expressions), whereas sentiment analysis mostly works with textual data only.
It's just as in common use. Sentiment is a superset of emotion, further including feelings, intuition, and rational conclusions drawn from past experience. Analysis is also a superset of recognition, which also includes taking emotions like contentment, happiness, humor affected, anger, rage, and passion and determining what sequences of them mean in the context of the scene or senario.