This may be a little contentious as it is a matter of formal vs informal usage of the word 'through'.
I believe that the proper spelling for the expression on these signs is 'Drive-through'. Hyphenated and formal.
McDonald's can't even seem to agree which way they want to use the informal - with or without a hyphen.
Others may argue that both these examples are for family fast food joints and by their very nature they are not formal establishments. I get that.
The flip side though is that these are serious businesses, and unless their usage of the informal 'thru' is a specific marketing angle, then it would be better for the English language to use the formal.
After all McDonalds goes as far as putting the acute accent on the 'e' in café, don't they‽