Food for thought...A grill is a surface that is broken by a piece of metal then an open(air) space..and on and on..'Like the grill surface on your back-yard grill.
A Griddle is a solid, flat surface, sometimes refered to in the restaurant business as a "flat top".
Indoors a stove with a true grill surface must be supported by an excellent venting system..one can imagine the smoke!!!
Some "griddles" have a smooth surface..(eggs, bacon, pancakes, etc.) and a ribbed side..(chicken, steaks, chops, veggies etc). that will give "grill" marks...I would look for one that had this double-sided feature.
I cannot comment on the ones mentioned above as I don't own them.
I can speak for Lodge Cast Iron griddles...they have (or did) two styles both of which I can highly recommend! After seasoning and use they become excellent tools! Be sure to measure your stove no matter what you buy!
And since this is my second post today about Lodge Cast Iron..Just for the record I am not under their employ!
Hope this helps!