This text uses America Centric definitions.
In America there are several different factions of liberals.
First there are the civil libertarian liberals, not to be confused with the minority rights liberals. These are the types most aligned with libertarians. Whether the issue is pornography, gay marriage, drug legalization, or prostitution, these are the ones (found in the ACLU or the Democratic Freedom Caucus) that agree with libertarians. They are very strong on civil issues, and slightly less on economic issues.
Then there are the union liberals. For them, protecting the working class is their motive. They are not overly concerned with civil issues, but are very concerned with protecting American Jobs. They aren't concerned about economic issues over much, but are quite interested in government regulation of the economy. Ironically this school of liberalism finds itself in alliance with one of the schools of conservatism, Mercantilist conservatism.
Then there are the environmental liberals. This faction is quite often at odds with the union liberal, as the environmental regulation proposed can quite often be harmful to the creation of jobs. While compromise makes all schools of progressive liberalism (except union liberalism) advocate the measure of environmental liberals to some extent, these are the core of that movement. They are not overly concerned with civil issues, but are quite interested in government regulation of the economy, just in a different way from union liberals and mercantilist conservatives.
Welfare Liberals are very much the core of American Progressive Liberalism. They range from the moderates of implementing a safety net to the extreme of a totally managed economy, all for the sake of helping the poor through taxation policy, government hand out policies, outright nationalization of portions of the American economy (such as health care), and regulation of the rest. While there isn't great concern for civil liberties here, economic liberties are completely dead within this tradition.
Finally there are also minority rights liberals. They are separate from civil liberty liberals for a reason, and that reason is the radicalization of this faction. Too many members of this faction are bigoted against groups outside their own minority. To hold up examples of the most extreme, look to Andrea Dworkin as an extremely radical misandrist feminist, or La Raza for Hispanic rights, or Louis Farakhan for African-Americans. They are quite opposed to both economic and civil issues as defined by classic liberals, and quite in favor of reverse discrimination.
There are also several smaller schools of liberalism.
Then there are several different factions of American conservatism.
Paleoconservatives, a smaller faction, are the one type which can be considered moderate libertarians. On economic matters they agree almost entirely with libertarians, and on civil matters they agree mostly.
Mercantile conservatives are the leading faction, and have been since the Republicans were called Whigs, and since the Whigs were called Federalists. Some may object that they should oppose government regulation when it harms their own interests, but that is not always the case. They dislike government regulation on themselves but accept it if it gives them an advantage. On civil issues they care little either way and are quite willing to advocate increased government control of civil matters in exchange for increased government control on economic issues provided that control gives them an advantage. While they are often seen as opponents of Union Liberals, they are often allies of Union Liberals. A tariff that increases the cost of imports protects American Industry (which satisfies the mercantilist conservative) also protects American Jobs (which satisfies the union liberal).
Moral conservatives are another major faction. While most exemplified by the Religious Right, it includes all those who advocate security above liberty. The moral conservative stands in distinct opposition with libertarians on civil matters. This school is not strong on economic thought, and is willing to exchange advocacy of government control of economic issues for advocacy of government control of civil issues. Any suggestion that drug laws or prostitution laws be loosened causes panic among this crowd.
Closely allied to the moral conservatives are the security conservatives. Like the moral conservative the security conservative stands in distinct opposition with libertarians on civil matters, and is not strong on economic though. While they lack the motive to police drugs or prostitution the way the moral conservatives do, they view any civil rights that impede police work as detrimental to society. While not strongly inclined by nature towards moral legislation the way the moral conservatives are, the fact that said legislation is law is enough to make them react with horror to any suggestion the laws be loosened.
Then there are the neoconservatives. These are the worst that conservatism has to offer. They are quite fond of regulation both economic and civil. They have no problems at all with a welfare state, since their ideology has a root with Trotsky. Because of that root, they have no problem with military adventurism, reshaping the world in their image in the spirit of Trotsky's "eternal revolution." They also have from Leo Strauss the belief in an elite that rules the ignorant masses, and from Machiavelli the belief that it is quite acceptable for leaders to lie to their subjects for the subjects own good. This, by the way, is the faction currently occupying the White House.
There are also lesser schools of conservative thought.
Then there are the factions of libertarians.
First there are the civil libertarian liberals, already described.
Then there are the paleoconservatives, already described.
Then there are the anarcho-capitalists, the most extreme form of libertarian. While most libertarians come out in favor of very limited government power, they come out against all government power.
Then there are the classic liberals, the core libertarians to the point where classic liberal and libertarian can be used interchangeably, who are considered soft by the anarcho-capitalists for our minarchism. This is by far the largest faction of libertarians.
Then there are the objectivists. While in agreement with classic liberals on almost everything there are a few key points of difference regarding the respect to be shown to those who disagree.
The leading schools of economic thought among conservatives are mercantilism, supply side / right Keynesianism, and some monetarism. Capitalism can be found among the paleoconservatives.
The leading schools of economic thought among progressive liberals are socialism, demand side / left Keynesianism, and some georgism. Capitalism can be found among the civil liberty liberals.
The leading schools of economic thought among libertarians are Capitalism, with traces of monetarism and georgism.