What's the difference between 打开 and 开门?
In the context of the example you posted, 开门 is describing the status of the shop. Like the meaning of 'open' and 'closed' signs you could find in most of stores. 

打开 in the context of the example you gave is describing the status of the door or anything could be turned on like window, valve or switch. This sentence should be translated to 'This door is open'.

Because in Chinese a word's meaning may varies according to the context and situation of the sentence. You should remember some combination of noun-adjective or verb-adverb but not just remember the meaning of a single word.