1. an encoder takes an input (e.g. text), and turns it into a numerical representation (e.g. an embedding).
2. a decoder takes an input (e.g. text), and then extends the text.
(There's also encoder-decoders, but I won't go into those)
These two simple definitions immediately give information on how they can be used. Decoders are at the heart of text generation models, whereas encoders return embeddings with which you can do further computations. For example, if your encoder model is finetuned for it, the embeddings can be fed through another linear layer to give you classes (e.g. token classification like NER, or sequence classification for full texts). Or the embeddings can be compared with cosine similarity to determine the similarity of questions and answers. This is at the core of information retrieval/search (see https://sbert.net/). Such similarity between embeddings can also be used for clustering, etc.
In my humble opinion (but it's perhaps a dated opinion), (encoder-)decoders are for when your output is text (chatbots, summarization, translation), and encoders are for when your output is literally anything else. Embeddings are your toolbox, you can shape them into anything, and encoders are the wonderful providers of these embeddings.
