The “Full-Service EDI” means that the process is being outsourced. The service here is not just about the translation of EDI but also performing end to end Order Processing system.
EDI or Electronic Data Interchange is a computer to computer data interchange process that deals with business documents formatted for business partners.
You can select any of the software and share that with your peer for EDI processing. An EDI Managed Service Provider can help you manage, implement your needs with processing the software