Mostly, experimental design is a large subject, which topic is the planification of experiments in general. Then factorial design is a sub-topic among many others within this large field.
For some authors, experimental design is about the plot layout, terminology coming from layout of experimental plots on land in agricultural experimentation. This will often include choice and construction of blocks.
Factorial design is then subtly different, it is about the layout of the various regressor variables, that is, how to combine/choose the possible values for the regressor variables. Literally, it is about how to construct the design matrix. The 'experimental design' then is about how to run this design matrix, for instance, how to do blocking, deciding the time sequencing of the runs (maybe by randomization) etc.
See also my related answer at Advantages/disadvantages of fractional factorial design vs completely randomized design where I wrote: Good books like Casella's Statistical Design make an important distinction between the Treatment design and the experimental design. Good experiments need both. To cite:
The title of this book, “Statistical Design”, was chosen purposefully.
Note that the title of this book is not “Experimental Design”. The
reason for this is that there are two pieces to a design, which we
separate into Treatment Design and Experiment Design. A Statistical
Design contains both of these pieces.