What's the difference with these two boxes?
Under what circumstances do I need to use a TLabel?
Under what circumstances do I need to use a TStaticText?
When choosing, what do I need to ask myself in order to make the right decision and place the correct control?
I'm going to answer your question from a Windows API point of view.
The problem with that kind of answer is that the LCL contains code that adds some features not present when using the Windows API (unless the programmer him/herself writes the code to implement them, e.g, hit testing on a non-windowed control)
The most important difference is that TLabel is NOT a windowed control whereas TStaticText is. Whether or not the control is windowed is the crucial difference that drives the choice.
Using that crucial difference to make the determination, the choice is driven by the following:
If there is a fair amount of text in the window (or "form" if you prefer) that doesn't need to be manipulated by the user then that text should be implemented as a TLabel. If the text needs to be "manipulated", e.g, moved around in the window by the user then using a windowed control such as TStaticText will simplify manipulating the control. The other important consideration is that since a TStaticText is in a window, the window that contains it can be thought of as a cocoon that protects the text, any painting that occurs _outside_ its window cannot affect the text in it (presuming some class/window styles are set accordingly.)
A non-windowed control does not have that protection. if anything is output at a location that overlaps the label text then the label text will be affected.
The LCL makes it a bit difficult to select one or the other because the LCL contains code that makes a TLabel (non-windowed control) have many of the features of the TStaticText (a windowed control) but, there is one difference the LCL (or any other code) cannot "compensate" for and that is: update speed.
A windowed control is always slower to repaint than a non-windowed control. Often, due to how Windows goes about repainting windows, the difference in speed can be quite noticeable. Even on fast machines, windows that contain many windowed control can be "elastic" when they are resized and, the reason is because of the large number of child windows the main window contains (e.g, MS Visual Studio.)
When text is implemented as a non windowed control, repainting that text will be quite a bit faster than repainting the same text in a windowed control. This makes updating/repainting the window quite a bit faster and makes the program feel more responsive.
The answer to your question is as follows: _in general_ use TLabel because repainting will be faster and it will consume less resources (it's not windowed), use TStaticText when that control offers some capability/characteristic TLabel does not offer that you really need.
HTH.