A student is anyone who is going to school at any level. An undergraduate is a specific type of student that has not yet earned their first Bachelors degree (years 1-4 at a major university.. or until they graduate). Students working on their Masters and doctorates are called Graduate students.

In American English, a student is anyone who studies. In terms of school, you are a student as long as you are taking classes! It is also a general term meaning someone who is learning or studying something. So, you can be a student of almost anything! Some countries/languages use the word "pupil", who is someone that has not yet graduated high school. So, while you are in elementary (Kindergarten to 5th grade), middle (6th-8th grade), or high school (9th-12th grade), you are a pupil. An undergraduate is a college student working towards a Bachelor's degree (4 years) or below (like an Associate's (2-year) or a certificate). Once you get your Bachelor's and you are still taking classes, you are a graduate student. Graduate students usually work towards Post-Baccalaureates, Master's Degrees, Doctorate Degrees, or even Post-Doctorate Degrees! Undergraduate level classes are usually labeded 1xx-4xx, with anything over 499 being a graduate level class. Then there is the case that a graduate student is taking undergraduate classes, meaning that they are taking classes for undergraduates, but they already have a degree. Similarly, undergraduates can take graduate-level classes, but they will still be undergraduates until they get a degree!

And as for undergraduate these words just have different origin

I think you can call anyone who is at at school a student ,while an undergraduate is a higher education one gets in a college.Hope not have misunderstood your question.

Difference depends on the country where the word is used. For example In some nations, the English term (or its cognate in another language) is reserved for those who attend university, while a schoolchild under the age of eighteen is called a pupil in English (or an equivalent in other languages). In its widest use, student is used for anyone who is learning.