Actually, no! Modern adware most often is, but there is a type of malware, initially called 'adware,' that has no binding to browsers or any other visible applications. It shows as a process in Task Manager, initiated by some hard-to-detect executable, but you will not see it in the list of running apps. The effects of such a program, running in the background, are common for adware: pop-up windows, panels, banners, etc. Moreover, other programs, besides browsers, can be classified as adware regardless of whether they are malicious.