Well both these styles surely do look exactly the same and in such cases the difference lies in the place of origin. So the English moustache is a style popularized by englishmen, as the name suggests but in reality this style is popularized by the depiction of Englishmen in Hollywood movies! The mistletoe moustache does not carry with itself such a heritage or popularity. It is a simplistic English Moustache and Mistletoe Moustache.
So while both are different styles they do fall in the same backed because the mistletoe is just a modern day English moustache. This is because the English moustache is longer than the mistletoe and also, it appears more uptight as well as loud as a style statement. You cannot possibly pull off either looks at workplace professionally but these are two cool styles for amateur moustache lovers because it does not require a strong moustache growth, rather just skilled use of trimmer and scissors!