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.
Text Embedding 3 is OpenAI's hosted embedding family, notable for letting the caller choose a shorter output vector than the model natively produces. It solves the storage problem directly: embedding indexes are sized by dimensions times vectors, so trimming 3072 dimensions to 512 or 256 shrinks the index substantially at a small quality cost. It exists because that trade is one the caller is better placed to make than the model author, and it removes the need to retrain to change it.