Like most terms in our field, the word "democracy" is also used in a wider and vaguer sense. But if it is used strictly to describe a method of government---namely, majority rule--it clearly refers to a problem different from that of liberalism [in the European 19th century meaning of the word]. Liberalism is a doctrine about what the law ought to be, democracy a doctrine about the manner of determining what will be the law. Liberalism regards it as desirable that only what the majority accepts should in fact be law, but it does not believe that this is therefore necessarily good law. Its aim, indeed, is to persuade the majority to observecertain principles. it accepts majority rule as a method of deciding but not as an authority fo rwhat the decision ought to be. To the doctrinaire democrat the fact that the majority wants something is sufficient ground for regarding it as good; for him the will of the majority determines not only what is law but what is good law.
--F. Hayek, The Constitution of Liberty, University of Chicago Press, 1960, pg 103-104
Then in an end note, Hayek quotes another author in a way that I think adds even further clarification:
Liberalism and Democracy happen to be two things which begin by having nothing to do with each other, and end by having, so far as tendencies are concerned, meanings that are mutually antagonistic. Democracy and Liberalism are two answers to two completely different questions.
Democracy answers this question--"Who ought to exercise public power?" The answer it gives is--the exercise of public power belongs to the citizens as a body.
But this question does not touch on what should be the realm of the public power. It is solely concerned with determining to whom such power belongs. Democracy proposes that we all rule; that is, that we are sovereign in all social acts.
Liberalism, on the other hand, answers this other question,--"regardless of who exercises the public power, what should its limits be?" The answer it gives--"Whether the public power is exercised by an autocrat or by the people, it cannot be absolute: the individual has rights which are over and above any interference by the State."
-J. Ortega y Gasset, Invertebrate Spain, quoted in Hayek, ibid, pg. 442
It is thus possible to consent to the political order (e.g. the use of majority rule) without agreeing to the rightness or justness of every majority decision.