The common Welsh word for the act of studying is astudio, and for the noun it's astudiaeth. Both of those are derived from the Latin studeo/studium which imply a zealous, painstaking striving for knowledge. The 1828 English and Welsh dictionary by Walters & Walters defines astudio as 'applying one's mind to the knowledge of a thing' and the 'engagement with books in pursuit of learning and knowledge'. There is a Latin-derived term for student (astudiwr) but it does not seem to be in common use (anymore - it is still in the 1828 dictionary but no longer in the modern dictionaries I consulted. Welsh speakers - feel free to correct me if I'm wrong!)
There are/were other Welsh terms for someone who studies: efrydydd is someone who brings things 'from his mind' (e-bryd). A llyfrgar is a bookish person (from the Welsh llyfr which is in its turn derived from the Latin librum for book). An ysgolhair is a scholar (from ysgol, derived from the Latin scholium from which we get 'school'). And darlleingar, finally, presumably has something to do with darllen, 'to read'. Most of these words, however, only appear in the 1828 dictionary and don't seem to be in common use anymore.
There is (or was) thus no lack of colourful terms for a person of a scholarly nature in Welsh. It strikes me as odd therefore that, instead of the Latin derivation from astudio or one of the other terms mentioned here, Welsh chose the term myfyriwr. There are a related verb (myfyrio) and noun (myfyrfa) but those don't seem to be in use, at least not in a formal learning environment.
I love the term myfyriwr, though, because the dictionaries agree that myfyrio means 'to ponder', 'to meditate'. This means that the Welsh student, rather than striving zealously for an external goal, rather seeks understanding through internalised contemplation. I haven't so far found a reason for this discrepancy, and of course having odd terms out among lists of common cognates is quite a common occurrence in many languages.
I find it amusing that the formal terminology for the act and concept of study in Welsh follows the majority of European languages which are all derived from the proactive and purpose-driven Latin studio (French: etudiant; German: Student; Spanish: estudiante; Dutch: student; English: student; Danish: studerende; Italian: studente; Portuguese: estudante; Swedish: student and so on - Irish goes instead for scolaire similar to ysgolhair). For the person studying in a university context, however, Welsh acknowledges the importance of understanding and meditation for the ultimate attainment of knowledge. In this goal-driven age with its relentless focus on assessment and outputs, that Welsh has retained a rather more contemplative and reflective term for learning provides makes me quite happy. (It also links in nicely with Kolb's learning cycle, which acknowledges a reflective period in each learning process.)