Secularism is the absence of religion, though not neccessarily opposition to or hostility towards religion.
A secular government is a government from which religion is absent.
A secular society is a society from which religion is absent, or largely absent, or at any rate regarded as not being very important to daily life. The U.S. may have a secular government, but it is not a secular society (although there are areas, such as parts of the Pacific Northwest, that are much more secular than the “Bible Belt”). Many European countries have much more secular societies than the United States. Ironically enough, the UK*, which in theory does not have a secular government–that whole Church of England thing, along with the head of state being Defender of the Faith–has a more secular society than the U.S. “Wall of Separation” of A.
Actually, it’s England that has the Established Church. Wales and Northern Ireland don’t; the (Presbyterian) Church of Scotland I think has some sort of status as a “National Church” but is not an “Established Church”.
Note that a secular society may not be anti-religious, it may even have a very high rate of very nominal adherence to some religion, like the Scandinavian countries where 90% of the population get married and buried in the Lutheran Church, but otherwise don’t really pay much attention to the whole religion thing. Religion may just be seen as a harmless, rather quaint, picturesque relic of the past. (In contrast to the feelings of many atheists and other nonbelievers in less secular societies; where large numbers of people still take religion very seriously, you are apt to have other people who take religion very seriously in a negative way.)
One can advocate a secular government (separation of church and state) without necessarily advocating a secular society, or one may of course advocate for both. The means of advocating may also be different; a secular government being something enforced by law and the Constitution, with a secular society being something to be worked for by way of peaceful persuasion and the voluntary decision-making of individuals (unless you’re some kind of Stalinist or something).
Then there is “pluralism”, which sounds more like what you’re getting at with this “moderating the relationship of multiple belief systems” thing. A society could be pluralistic but not secular–made up of devout members of multiple faiths. Or pluralistic and mixed between secular, devout (of multiple faiths), rabidly atheistic, etc. (Like the U.S., in other words.) In any event, pluralistic societies are well advised to have secular governments, so as to avoid the whole “holy war” thing.