I have worked on .NET, JAVA, Wordpress, Sharepoint and PHP applications in different domains and found that for Blackbox testing there is no difference in the testing methods for Manual testing. Unless you are not bothered about the test environment, Once a build is successful, deployed and ready for testing, you are ready to execute your same test cases.
One of the application I worked in, is having older version in Wordpress and newer version where whole application was re-builted was in JAVA, first we tested the Wordpress application (for its 2 releases and then JAVA application from scratch). The only difference was we learned from the client bugs of Wordpress application and modified our test cases to cover the scenarios which were not covered earlier and executed the same on JAVA version. Only the approach over which test cases were built was modified as executing same test cases with same approach wouldn't have changed anything (Pesticide Paradox).
Methodologies always remains the same i.e. independent of technologies, else while providing definition of Methods you must have seen disclaimers that this testing method is for .NET and JAVA, not for PHP and Wordpress. Since such disclaimers are not there, it means they are generic.
Yes, for some NFRs testing like Security testing your testing methods will depend upon the technologies being used.