It's the same thing, but "hometask" is not actually a correct word in English. "Homework" is what the teacher gives for you to do "at home." (outside of class) and if you were doing chores around the home (like laundry/cleaning) we call this "housework" (or "housekeeping")

"Hometask" really isn't a word in English. We only say "homework". "Housework" includes the jobs and chores that you regularly do to maintain and clean your home.

I have never heard of "hometask" either. Did your teacher actually use this word? It sounds as if it should have the same meaning as homework.

Can you give an example of a 'hometask'? I've never heard that before.

The term “home task” is often overused by the East Slavs. Bearing that in mind, a British linguist named John Stephenson said: “The standard term for ' домашнее задание ' in the UK is 'homework' (one word, uncountable). […] If homework consists of several tasks, people in the UK would normally refer to each task as 'a homework task' or 'a homework assignment'. 'home task(s)' […] appears to be in use on a few UK nursery and schools' websites, usually to distinguish them from 'classroom tasks'. 'home task(s)' is also used by the UK Department for Education (Мин-во образования) and the Office for Standards in Education (Ofsted), the UK govt body which inspects schools. However, in both cases it appears to mean the same as 'homework tasks', which is much more common. Also […] 'home tasks' could in some cases be misunderstood to mean 'tasks performed at home' generally, including making meals for the family, washing clothes, feeding the dog etc, all of which we call 'housework' rather than 'homework'. Why use the little-known and ambiguous term 'home task' when everyone understands exactly what 'homework' and 'homework task' mean, namely 'tasks given by a teacher/school/college/university to a schoolchild/student to carry out at home'? Note that I can only speak for the UK, not for the USA/Oz/NZ/Can etc. However, 'homework' is a commonly-used word in the United States with the same meaning as in the UK.” No wonder there’s no “home task(s)” in the BNC, dictionaries or thesauruses. There are hardly any websites that use this collocation. To sum up, the term “home task” is unimaginably rare and quite ambiguous, so using it is neither safe nor recommended. If you can read Russian, here is an insightful discussion of this matter (starting with the comment of Shabe, 19.12.2021): https://www.multitran.com/m.exe?a=2&l1=1&l2=2&page=10000&MessNum=338758.