E5 is an embedding model family trained on large collections of weakly supervised text pairs, with the task described in the input so one model serves queries, passages and classification. It solves the problem that an embedding model trained on one kind of pair transfers poorly to another. It exists because describing the task in the text is a cheap way to make one model cover several retrieval settings.
Nomic Embed is an open embedding model released with an open training dataset and reproducible training run, as well as long-context support. It solves two problems at once: most open embedding models publish weights but not the data they were trained on, which makes their behaviour hard to reason about, and most cap inputs short of a document. It exists because an embedding model whose training data is inspectable can be evaluated for the biases that come from that data.