The results of the Scribbr Plagiarism Check will be 99% the same as the Ephorus check used at your school. The Scribbr Plagiarism Check is optimized for students, which means that you will receive a detailed report with extra information to fix and prevent plagiarism.
Schools often have their own database of (prior) theses. Scribbr has no access to those databases. When you copy data from another thesis that is not publicly accessible, the Scribbr Plagiarism Check will neither be able to detect plagiarism nor identify the source of this data.
However, most theses are actually publicly accessible since many universities and schools have public databases. This means that the Scribbr Plagiarism Check is able to find these theses.