TBGRABitmap.TextSize doesn't take into account the kerning while TBGRABitmap.TextOut does.

The kerning is for example that "T" and "e" and be put closer because they fit together. So the result of TextSize can be bigger than the actual text width.

TBGRABitmap.TextOut relies on TCanvas.TextRect function, which relies on LCLIntf.DrawText (see forum thread). The latter can be used to get a measurement that takes into account kerning.