I would say YES, there is a class gap in the wizarding world.
But it isn't as defined by the Muggle world. The 'classes' you refer to in the Muggle world are demarcated solely on money. People socialize only with people of similar spending capacity (barring exceptional circumstances).
The wizarding world is rather different. Janus Bahs Jacquet got it kind of right. The demarcation in the wizarding world is in terms of their beliefs on 'blood purity' rather than the actual ancestry of the witch/wizard. The 'pure-blood' supporters are completely anti-Muggle. They despise anything to do with Muggles (from Muggle-born witches/wizards to Muggle technology). According to the Pottermore article on Pure-Bloods:
Slytherin's discrimination on the basis of parentage was considered an unusual and misguided view by the majority of wizards at the time. Contemporary literature suggests that Muggle-borns were not only accepted, but often considered to be particularly gifted.
...
Magical opinion underwent something of a shift after the International Statute of Secrecy became effective in 1692, when the magical community went into voluntary hiding following persecution by Muggles. This was a traumatic time for witches and wizards
...
Under such conditions of uncertainty, fear and resentment, the pure-blood doctrine began to gain followers. As a general rule, those who adopted it were also those who had most strenuously opposed the International Statute of Secrecy, advocating instead outright war on the Muggles.
However, plenty of supposedly 'pure-blood' families condemned this school of thought and believed that one's ancestry had nothing to do with the witch/wizard in question. These include the families of Weasley, Longbottom, Abbott, Crouch,etc.
These families, along with the rest of the wizarding world belong to the other 'class'. They all know and socialize with each other, as evidenced by the Muggle camp manager's remarks at the site for the Quidditch World Cup:
“It’s like some sort of . . . I dunno . . . like some sort of rally,” said Mr. Roberts. “They all seem to know each other. Like a big party.”
Harry Potter and the Goblet of Fire Chapter 7: Bagman and Crouch
Wealth doesn't matter to these 'classes' of people. All that matters is whether you are bigoted or not.
While it does seem like wealth does matter to the other 'class', canon only says the Malfoys and Blacks are incredibly wealthy. There is no evidence to suggest the Goyle family or the Crabbe family were rich. Just that they believed all Muggle-borns (or Mudbloods as they like to call them) are scum, and that the Muggles deserved to be subjugated to rule under magic folk (pure-blooded at that).
