Yes, either of these certifications would comply with OSHA’s standard, assuming they meet the other requirements of the standard. To comply with OSHA’s standard, certifications must include the type of crane for which the operator is certified, but a certification may also include other information such as the lifting capacity for which the operator is certified. OSHA simply removed the requirement that certifications include the lifting capacity.
OSHA is aware that there are certification organizations that still include the type and capacity of the crane on which an operator is certified. This form of certification continues to be valid. See also OSHA’s temporary enforcement policy regarding crane operator certification after November 10, 2018 that is accessible from the Cranes and Derricks in Construction webpage.