adopt -> you take something (e.g., a psychometric scale) and use it as is (without changing it)
adapt -> you take something and modify it to suit your specific use (e.g., you change items in, or add new questions to, an existing psychometric scale)
Adopting the scale means that the researcher uses a scale previously prepared by other researchers in previous studies and applies it to the research sample without making modifications to its paragraphs or extracting its validity and stability. Either adapting the scale is using a scale from previous studies, but the researcher modifies its paragraphs in proportion to the age characteristics of the sample and their environment. With a number of other procedures
The two words are used in psychometrics similar in their literal meaning. Adopting a test tool means using it without changing anything, from the indicators (statements), domains (factors) if included, as well as the scoring and interpretation system or the norms/standard that go with the tool. On the other hand, adapting a test tool is making some modifications in any part of it to suit the characteristics of the target samples of participants. In this case, face validation and reliability measures through pilot testing is necessary to make sure that the modifications made are suitable to the participants of the research to be conducted.
Adopting is directly taking the tool from one standardized source, while adapting is taking the tool after reviewing different sources/literature, and it may have more than one source.