Actually, even most Japanese people don’t really know the meaning of Edomae sushi (or Edo-style sushi) . The “Edo” in Edomae is the former name of the present-day Tokyo, and “mae” means “in front”. In other words, Edomae means “in front of the town of Edo”. Exercising our imagination a bit more, this probably referred to the Edo Sea, currently known as Tokyo Bay. This is probably still a bit confusing. To broaden our perspective a bit more, how about we use analogical reasoning of the Edo Sea and sushi, and define it as sushi that uses fish caught in the Edo Sea? I think you understand now. To put it simply, this is sushi created in Edo, during the Edo period. Therefore, “Edo period sushi” shortened to “Edo sushi” would have been an acceptable name as well. But we can’t leave out the “mae”. This is because the word “Edomae” is rich with meanings.
The difference between Edomae sushi and Edo-style sushi is simply the preference of the translator. Also, the difference between Edomae sushi and Edomae zushi is that when the two parts X (Edomae) and Y (sushi) are said together XY (Edomae sushi), the voiced sound “su” at the beginning of Y changes to the unvoiced sound “zu” according to a Japanese phoneme rule. Both these words have the same meaning.