Maybe more detail than you wanted but I think it helps to know the history of the party name.
The Liberals were (with the Tories (AKA The Conservative Party)) one of the two great parties of the 19th Century. They helped to usher in many of the great (Liberal) reforms that transformed Britain from an aristocracy into a democracy. Hence: The Liberal Party. The Liberals went into decline starting in 1918 and the newly ascendant Labour party edged them out of the top two. They have been in the political wilderness ever since.
Labour started out as the working man’s party and were helped into power, ironically enough, by the Representation of the People Act passed by the last Liberal prime Minister in 1918 which gave the vote to all adult men for the first time. Labour was officially (and in reality) a socialist party working towards “the common ownership of the means of production, distribution and exchange” until the Blair reforms of the 90s. Corbyn wants to take them back there which is why he causes so much trepidation among the moneyed classes.
For most of the 20th century, power alternated between the (capitalist) Conservative Party and the (socialist) Labour Party. The Liberals were squeezed in the middle but it’s not really fair to call them a centrist party because politics is not one dimensional. They are certainly not Libertarian. If anything, they are the opposite.
In the early 80s, the Labour Party had drifted way over to the left in response to the rightwing shift of the Tories under Thatcher and a bunch of breakaway Labour MPs formed a new party — The Social Democratic Party (SDP) to escape the nakedly socialist Labour Party and take advantage of the empty centre ground.
During this timeframe, the Liberal Party were languishing at an all time low but, still, there was not enough room for two parties in the centre and the Liberal Party and the Social Democratic Party merged to become the Liberal Democratic Party, AKA the Lib Dems.
I wouldn’t draw too many inferences from the names of the parties.
The Conservatives were once conservative but no longer; they have become a radical, nationalist, neoliberal party. More Ayn Rand than Milton Friedman.
Labour was once the party of labour. They still are to some extent (for example, most of the Trades Union are affiliated with the Labour Party) but it’s not clear that this association will survive Brexit. As with the Democrats in the USA, Labour is now an odd mix of blue collar workers and educated people of the left, often dismissed as Champagne Socialists. If Corbyn has his way, they will go back to their socialist roots (he has plans to renationalise several industries) but it’s not clear that he will survive long enough as leader to make that happen.
The Liberals chose their name when liberals stood for democratic reforms and individual freedoms. The word “Liberal” really meant something back then and bears little relationship to what Americans (or Australians) mean when they say “Liberal”. Social Democracy is a real thing in most of the world outside America and that’s what the SDP stood for. The name “Liberal Democrat” is an accident of history and it doesn’t pay to read too much into it.
The Lib Dems of today are internationalist, environmentalist and oriented towards local control. Even in their wilderness years, Liberals and LibDems have been a major player in local government. On economic issues they are somewhere in the middle, but that doesn’t even begin to capture what they stand for.