While you could identify some points of vague commonality, the 'Liberal Democrats' in the UK do not meaningfully correspond with liberal 'Democrats' in the USA. There is an even greater divergence between American and continental European understanding of the word liberalism.
"Today the word "liberalism" is used differently in different countries
. One of the greatest contrasts is between the usage in the United States and usage in Continental Europe. In the US, liberalism is usually contrasted with conservatism, and American liberals support broader tolerance and more readily embrace multiculturalism and affirmative action. In Europe, on the other hand, liberalism is not only contrasted with conservatism and Christian Democracy, but also with socialism and social democracy. In some countries, European liberals share common positions with Christian Democrats."
"Racism is incompatible with liberalism. Liberals in Europe are generally hostile to any attempts by the state to enforce equality in employment by legal action against employers, whereas in the United States many liberals favor such affirmative action. Liberals in general support equal opportunity, but not necessarily equal outcome. Most European liberal parties do not favour employment quotas for women and ethnic minorities as the best way to end gender and racial inequality. However, all agree that arbitrary discrimination on the basis of race or gender is morally wrong."
Or as explained by an American academic Gerald F. Gaus in Stanford's Encyclopedia of Philosophy:
"Liberalism can be understood as (1) a political tradition (2) a political philosophy and (3) a general philosophical theory, encompassing a theory of value, a conception of the person and a moral theory as well as a political philosophy. As a political tradition liberalism has varied in different countries. In England — in many ways the birthplace of liberalism — the liberal tradition in politics has centred on religious toleration, government by consent, personal and, especially, economic freedom. In France liberalism has been more closely associated with secularism and democracy. In the United States liberals often combine a devotion to personal liberty with an antipathy to capitalism, while the liberalism of Australia tends to be much more sympathetic to capitalism but often less enthusiastic about civil liberties. To understand this diversity in political traditions
, we need to examine liberalism as a political theory and as a general philosophy."