Some quotes mention IEC 62619 and UN38.3. Others don’t. Is that why prices differ?

Often, yes. Certified batteries require third-party testing (IEC 62619 for safety, UN38.3 for transport). That costs money and the supplier passes it on. Uncertified batteries skip this step and are cheaper — but they may be blocked at customs in your country (Kenya KEBS, Nigeria SONCAP, Brazil INMETRO) or rejected by insurers in Europe. The “cheap” battery can become very expensive if it cannot clear customs or get insured.