These two words describe different activities, and in this industry the difference is not pedantry.
Certification
A certification body assesses your management system against a standard and issues a certificate. This is what happens with ISO 9001, ISO 14001, ISO 45001, ISO 13485 and ISO 27001. The certificate says your system conforms to the requirements of the standard.
Accreditation
An accreditation body gives formal recognition that an organisation is competent to carry out specific tasks. This is what happens with laboratories under ISO/IEC 17025, inspection bodies under ISO/IEC 17020, and medical laboratories under ISO 15189.
Accreditation also applies one level up: certification bodies are themselves accredited, by bodies such as ANAB or IAS, which is what makes their certificates meaningful.
Why the distinction matters practically
A laboratory is accredited to ISO/IEC 17025, never certified. An organisation describing itself as “ISO 17025 certified” is telling an assessor something about its own understanding.
The substantive difference: certification assesses conformity to a system standard. Accreditation assesses technical competence to produce valid results — meaning the assessors examine methods, measurement uncertainty, equipment, and the qualifications of the people doing the testing, not just the management system wrapped around them.
One useful filter
If you are choosing between advisers for laboratory work, how they use these two words tells you a good deal before you have asked a single technical question.