No. Hash functions are also used for verification.
Probably the simpliest example: Checksums [2] (e.g. Message Authentication Code (MAC)).
I would like to say, that for digital signatures the common software is [EC]DSA logic, and sha256 (or other hashing) is seldom used for signatures. Next to the (H)MAC functions (as described above by bob123), the main benefit and use case of sha256 (and other hashing software) is, that you can say, if content of a file/data has been changed. E.g. you transfer data from system A to B. And also you provide the short checksum. Then B can run the sha256 also on the file, once received, and must receive the exactly same hash value. Otherwise file has changed.
Thanks, I never thought of that. So using Hash functions as checksums is more important in this context. Even if there is no bad intention from any party involved in the process, computer bugs, corrupt data, or similar problems can always occur. Therefore it is important to check the integrity of the data.