I don't think the kanjis for ''Da'' and ''Moto'' look like the kanjis you mentioned. At least I can tell which one is the correct one.
I think when written on the forum it is easy to tell, but on the lantern with fancy calligraphy there is no bottom enclosing line on the box. So it looks like a type of Kanji with a 3-sided box.
I think it's sort of like the difference between cursive English and typed lettering. Sometimes it can be harder to read someones cursive handwriting even if you know English well!
I see, but I think that in that case, you may want to practice the cursive letter and kanjis when you want to write them.
But you made a good point there, soudou!