она не есть кошка vs у неё нет кошки
Are these equivalent? Or is one of them wrong?
One of them is from google translate, I'm pretty sure the other one was in this course.
I've seen funnier things in Google Translate, I'm telling you. You probably want to exercise a great deal of caution with it.
It is used with some abstract nouns, in set expressions and in formal/official style.
Or maybe you are writing in a rather neutral style but decided to compose a particularly convoluted sentence with clauses. You may try phrasing your sentence using nothing and «есть» or use «являться»,«иметь» and «иметься». In particular, if you are OK with being bookish, you might want to use a participle. Naturally, you cannot form a participle if you do not have a verb.
- Были начаты проекты, не имеющие аналогов в истории города. ~ The projects were started that have no equivalent in the city's history.