GTE is a family of text embedding models trained for retrieval, with variants covering English and multilingual use and long inputs. It solves the same problem as the other retrieval-focused embedding families: a general-purpose encoder is not optimised for the asymmetric comparison of a short query against a long document. It exists because retrieval quality is decided at the embedding step, and a family that scores well on public retrieval benchmarks is the cheapest way to improve everything downstream.
Instructor embeds text together with an instruction describing what the embedding is for, so one model serves retrieval, clustering and classification without fine-tuning for each. It solves the problem that a single fixed embedding cannot be optimal for several different tasks, and fine-tuning a copy per task is expensive and easy to get wrong. It exists because telling the model what kind of similarity you want is a cheap substitute for training it to want that.
