The characters' names, most of the their appearances, and some other general aspects about them are the same. The tone, themes, and story lines are very different.
Some spoilers follow
Many of the characters in Riverdale have names, appearances, and general personas and relationships that mirror their comic book counterparts. This is especially true of the four principle characters.
- Archie was a popular, athletic, red-haired kid in the comics;
- Veronica was a dark-haired and fashionable rich girl;
- Betty was a blonde, down-to-Earth girl next door;
- Jughead was a dark-haired underachiever from a working class family.
At the beginning of the TV series, they toyed with an Archie-Betty-Veronica love triangle that was a staple plot line of the books, but they quickly abandoned it to make Betty Jughead's love interest. Many of the secondary characters also appeared in the comics, like Moose, and Reggie, and Cheryl Blossom. Miss Grundy is a bit of a curveball because you initially believe her to be a beautiful young teacher in the show when she was an elderly woman in the comics... but later you learn that the young woman murdered the real Miss Grundy and they show a picture of the real teacher as an elderly woman wearing the same dress she wore in the comics.
Some characters veer sharply away from their comic personas in certain ways. In the comics, Jughead was kind of dumb (played for laughs) and he rarely took anything seriously. Hiram Lodge was not a crime boss in the comics. Moose was very dumb, and not gay.
Archie comics have been around since 1941 and for the bulk of its run time, it has been pretty tame in terms of adult themes. Most Archie comics dealt with humorous events in the life of American high school students. Some of them toyed with more adult story lines, like Archie and the gang thwarting Soviet spies and the like. They did not normally deal with such themes as serial killers, sexual relationships, drugs, gangs, homosexuality, or abusive parents--and if they did, never so directly. Around 2010, you started to see more modern sensibilities and adult story lines incorporated into the comics, such as the introduction of a gay character. The comics have always been overwhelmingly upbeat and light-hearted in nature, even when they did deal with such issues. Riverdale's dark tone is a big departure from the comics.
Archie comics characters were less diverse than the show's characters. Veronica Lodge (as her last name suggests) was not Latina, and her father was an elderly white businessman. Reggie was not Asian. Josie and the Pussycats did have crossover adventures with the Archie gang, though only one of the Pussycats was black (Josie and the other were white). Of the characters depicted on the show as homosexual, only Kevin Keller was gay and Toni Topaz was bisexual (both comic characters introduced in 2010 or later).
The show makes occasional callbacks to things from the Archie comics and cartoon shows, such as Josie and the Pussycats singing Sugar, Sugar with the Archie gang, and playing with Archie on guitar.
If all of the character and place names (and very specific costume choices like jughead's crown-hat) were changed, it would take a very observant person to begin noticing similarities between the four main characters in the show and the four main characters from the comics. Change the hair colors, and it would be more or less impossible.