Yes there is. Neo-Nazism refers to any social or political movement wishing to revive National Socialism post WWII. Often, especially internationally, those who are part of the movements do not use the term to define themselves.

Martin Frost, Neo-Nazism

Neo-Nazism does differ from traditional national-socialism and is not limited to a single political concept. That is, it includes everything from Strasserism to Hitlerism or white supremacism (which traditional national-socialism wasn't, as it was ethno-nationalism based on the Germanic people) in general.

As already said, "neo" is a shortened form of the Greek word "neos" meaning new and became used to describe any (radical) group fitting the description mentioned above. Most of the current day groups in Western Europe and the United States that are called neo-nazi are related to Hitlerism, where specific conceps from national-socialist Germany, and the SS in particular, are taken and romanticized, often coated with Holocaust denial and strong antisemitism.

Other organisations reject Hitlerism and simply focus on a more "neutral" description of national-socialism, which you often see in Russia for example where the concept is basically the same as the program of the NSDAP, but with Russians instead of Germans. These groups then oppose the neo-nazi ones mentioned above for supporting Hitler and his party which enabled an almost genocidal war against the Soviet population during World War II. In fact, this has even led to a unique political movement, named National Bolshevism, though less radical ideas are far more wide spread as well.

Ergo, neo-nazism is a general term describing a variety of movements which base themselves on, or want to revive, (specific concepts of) national-socialism - and the left or right wing faction of the NSDAP - often combined with additional ideas including, but not limited to, white supremacism (in Europe and the United States), ethno-nationalism and Holocaust denial.

You may find this post relevant. Here, the author makes the case that fascism was a political movement unique to the early-20th century.

Considering that many historians consider nazism to be a form of fascism, I don't think that it's unreasonable to say that nazism of Hitler's day is not the same as neo-nazism today for a lot of the reasons that /u/depanneur mentioned.