There are a number of issues here.
First, applications can support a variety of rendering methods, e.g. OpenGL and software rendering. If an application renders in software, then no hardware acceleration will be used at all (or minimally, e.g. for blitting operations etc.); this is usually what happens when you select software rendering in applications which support it (Chrome, many older games). If an application renders using OpenGL or something like that, acceleration will depend on the available hardware and whether the appropriate drivers and libraries are installed. In most cases you’ll get hardware acceleration, especially if you’re using GNOME 3 since that requires hardware acceleration (so if GNOME 3 starts in non-classic mode, you’re sure that some form of hardware acceleration is available).
Second, on a system such as yours with two GPUs, acceleration can be provided by either the integrated GPU, or the dedicated GPU. This is generally not controlled by applications, but by the kernel, using the VGA switcheroo. Recent versions of GNOME have support for launching applications using either the integrated GPU or the dedicated GPU explicitly; that’s what the “Launch using Dedicated Graphics Card” option determines (see this blog post for details). If you start an OpenGL application “normally”, it will be hardware accelerated, using your integrated (Intel) GPU; if you start it using “Launch using Dedicated Graphics Card”, it will be hardware accelerated, using your dedicated (AMD) GPU.