Is it discrimination to hold someone from a minority or underprivileged background to the same academic standard as regular students? Suppose a graduate student is found to be noticeably or even significantly behind in overall academic and research competence. For example, they may have significantly weaker language and comprehension skills and technical skills such as using a computer or navigating the web. They may also be lacking other peripheral skills which are often important for graduate students. This may be indirectly related to being from a minority and/or underprivileged background where such exposure and opportunities to learn can be limited. 

If he/she are held to the same standards as his/her peers when comparing their relative performance, would this be considered to be discrimination if his/her situation was known? On one hand, same treatment would be fair to his/her peers and avoids human judgement. On the other hand, one could argue that it is unreasonable to expect the same amount of performance when they are missing necessary skills and experience. 

There was a comment that 'held to the same standards' was too vague. As a result I want to provide some hypothetical situations in which it is necessary to compare the performance of a student with his/her peers.

Suppose an advisor has limited funding for RA and travel opportunities. They want to provide them to students with the best performance either as a means of rewarding them or to provide a better return on investment. This would mean the graduate student in question would have little chance of obtaining it. Is this discrimination or an unfair bias? 

Suppose again the average graduation time for a program is 5 years. However, due to the slow progress of the student (compared to their peers) they may be held for 6 or 7 years before being deemed ready to graduate. Is this a discriminatory practice?
You are asking two separate and completely unrelated questions. The first, which you posed in the title, concerns the meaning of the English word "discrimination". The answer to that question is very simple: no, treating all students according to uniform standards and policies without consideration of their membership in various ethnic or racial groups is not discrimination; rather, it is precisely the absence of discrimination. That says nothing about whether it is a good or a bad (or moral/immoral, ethical/unethical etc) policy, it simply answers the question of whether it fits the meaning of a particular word in the English language.

Your second question was about how graduate students from minority and/or underprivileged backgrounds "should" be treated, which I interpret as asking about whether the policy of applying uniform standards to all students alluded to above is a good or a bad thing to have. This is a special case of a large set of questions associated with the terms affirmative action and reverse discrimination. It is a controversial topic that has been and still remains the subject of a large amount of debate as well as litigation, and if you care to learn more about it, there's a large body of discourse on such questions that you can find referenced in the Wikipedia articles linked above or with a google search. It is a sufficiently complex topic that I feel I can't meaningfully comment on it in a short post, and in any case enough has been said about it by people who have given the subject much more thought than I have to make anything I can think of saying about it laughably simplistic and uninteresting.

To clarify, this answer expresses no opinion about what policies should be in place for treating graduate students from underprivileged backgrounds.