formal equality — the rules, criteria, process, etc. do not explicitly discriminate
substantive equality — the effect of the rules, criteria, process, etc. is non-discriminatory
Most sports involve formal equality. In a professional baseball game, we want the rules to apply to both teams in the same way, even if this means one team is much more likely to win than the other. But in amateur golf, handicap may be used to give players of different skill levels a roughly similar likelihood of winning; this is a form of substantive equality.
Early women's rights supporter John Stuart Mill argued in favor of formal equality:
"It is not sufficient to maintain that women on the average are less gifted than men on the average, with certain of the higher mental faculties, or that a smaller number of women than of men are fit for occupations and functions of the highest intellectual character. It is necessary to maintain that no women at all are fit for them, and that the most eminent women are inferior in mental faculties to the most mediocre of the men on whom those functions at present devolve. For if the performance of the function is decided either by competition, or by any mode of choice which secures regard to the public interest, there needs be no apprehension that any important employments will fall into the hands of women inferior to average men, or to the average of their male competitors. The only result would be that there would be fewer women than men in such employments [....]" — from The Subjection of WomenIn Mill's day, the laws did explicitly discriminate against women. So the least a reasonable society could do, he argued, was to take away these formal barriers and let the skill and strength of individual women be measured against male competitors. Today, formal discrimination against women is (usually) unthinkable in western democratic societies. Yet formally non-discriminatory policies can have discriminatory effects against women. One motivation behind the Family and Medical Leave Act was to help with the situation where women have to choose — in a way men do not — between having children and continuing their careers.
Perhaps the most famous snarky remark about formal equality came from Anatole France:
"The law, in its majestic equality, forbids the rich as well as the poor to sleep under bridges, to beg in the streets, and to steal bread."(A good quote to recite the next time someone points out that both heterosexuals and homosexuals are forbidden to marry persons of the same sex.)
Another area where the distinction between formal and substantive equality comes up is voter ID legislation. A formally fair process (ID required to vote) can have discriminatory effects (fewer poor or even fewer blacks voting). It's not enough to cite formal equality and brush off the complaint. If there is an imbalance in effect, we need ask if formal equality is all we really care about — as with professional baseball teams — or whether we're concerned enough with the substantive inequality to do something about it.