An often-offered definition of the difference between Anthro and Furry is that Furry is a sexualized form of Anthro, whereas Anthro is simply drawing animals acting like humans and sipping tea; ergo, Anthro is the 'true' art and standard of civilization, while Furry is its mentally retarded drooly cousin, mostly consisting of cub porn and recolored Sonic OC's.
This is the most widely accepted definition between Furry and Anthro. It's also dead wrong.
To help demonstrate this, I've made up a simple graph to make it clear what 'Anthro' is and what Furry isn't:
A brief explanation of the relevant bits so I'm not just repeating what's already written on the chart's deviation page:
Anthro covers every possible thing you could turn into a humanoid.
Anthro Machines are Droids.
Anthro Plants are Treants.
Anthro Animals are Furries.
Anthro anything else is . . . whatever you want to call it, it's not really important which.
In case you didn't notice it when you first saw the chart, the style, the context, and the genre are completely and utterly irrelevant. There is no delineation or special terminology given to obscene materials in that chart, or for cartoon characters, or for realistic representations of these concepts. There's a good reason for that.
If you are drawing ANY representation of an animal given human traits, it's Furry. It can be Mickey Mouse, It can be Sonic, it can be Hepcats fanart, it can be that Aflac duck . . . I don't care how sexualized or innocent, how cartoony or realistic, how crude or refined, if you are drawing animals doing things that you don't see animals doing in real life, it's Furry.
Attempting to classify yourself as Anthro when you're drawing Furry is deception at best and arrogance at worst deception because while all furry is anthro, not all anthro is furry, and arrogance because it furthers this idea that drawing animals is okay only as long as it's within socially acceptable boundaries and you're not doing anything crazy like pretending you were a dragon or giving your catgirl the build of a college coed.
Yes, there are seedy elements of Furry, just like there are artistic nudes on DeviantArt. There is drawn pornography (commonly termed 'Yiff') in Furry, just like there's Hentai in Anime. There are plenty of Furry archives that will push these limits, just like there's other art archives out there that will post all the other stuff DeviantArt doesn't allow. There is no excuse for claiming all Furry is Yiff, just like there is no excuse for claiming all Anime is Hentai. (For those who have short memories, the Anime/Manga/Hentai connection was a common mistake in the 90's, but this too has died down thanks to the mainstreaming of Anime and Manga.)
Unless your animal characters are little plush toys, art sculptures, or some other series of inanimate objects that have somehow come to life, you are dealing in Furry and if said items have any human traits whatsoever, they're still Furry. The sooner we all accept this fact and stop treating the term 'Furry' like it only applies to the kinky fetish side of Anthro . . .
. . . the sooner we can get the rest of the internet to cut us some slack.