"No, that is not right."
違う (ちがう) is a verb meaning: (1) to differ (from), to vary; (2) to not be in the usual condition; (3) to not match the correct (answer); (4) to be different from promised. Source: https://jisho.org/search/%E3%81%A1%E3%81%8C%E3%81%86
The ~います ending is a form of the root verb (one drops the ~う when conjugating a verb).
ちがう is dictionary form and ちがい is another word entirely, if it's even a word. The problem with duo is it splits the conjugation into seperate tiles, making the different parts of words look like seperate things. All る verbs end with る and all う verbs end in an う syllable (う, く, む, つ, す, etc.) Standard conjugation is remove る for る verbs, and change from う syllables to い syllables for う verbs, then add ます for present tense positive or ません for present tense negative. ねる(sleep) becomes ねます(to sleep) or ねません(to not sleep). さがう(be different) becomes ちがいませ(to be different) or ちがいません(to not be different). Obviously there are other forms of conjugation, but I'm still learning and those forms haven't been covered yet at this point in the lessons.
The main source of confusion here is this: ちがい (difference) is a noun, but ちがう (to be different, be different) is a verb. With nouns you have to use copula です. So in this case, when I see ます, I know that it cannot be noun, therefor the basic form is ちがう (verb). You can say 違いです, but the literally meaning would be "is the difference", for example これは違いです would mean "This is the difference.". 違います (verb) is an expression, literally "it differs".
1 is for saying a fact is wrong e.g. これはリンゴですか - 違います、ナシです (It is about a fact is right or wrong, so そうじゃないです/そんなことないです cannot be used)
2 is for saying a method/happening is wrong (referred by そう - that way) "It is not that way" e.g. 公園に行きますか - そうじゃないです（違います is also ok because it is also a fact）、銀行に行きます (It is something future, so そんなことないです cannot be used)
3 is saying if there is such a happening "そんなこと" or fact. It is not right or wrong, it is about a fact exists or not. きれいですね。 - そんなことないです "What you said doesn't exist" (much softer than 違います which says it is wrong)
It is the non-past polite conjugation of the verb 違う meaning "to differ"
違います - "it is different" (that thing is different than the correct thing, it is not right)
違いです would use the noun form 違い meaning "difference, discrepancy, error" with the copula です(is/am/are) and would mean "It is an error/it is a difference", which has a slightly different use.