Sex, Drugs, Abortion, Foreign policy, Size of government (one want huge state government the other huger federal), Resp0onsibility, Religion and about everything BUT taxes.
Libertarians, as a group, take no position on sex other than it is none of the federal government's business. Liberals want government to set the rules liberals want re sex and how it is expressed.
Libertarians, as a group, take no official position on abortion other than it should be a local matter of conscience and the federal government has no constitutional authority to regulate it in any way. Liberals want the federal government to make abortion legal everywhere for everybody, period.
Libertarians, as a group, take no official position on foreign policy other than the federal government should be strictly limited to its constitutional authority when it comes to foreign policy. Liberals put no constitutional restrictions on much of anything.
Libertarians, as a group, take no official position on drugs other than it is appropriate for the federal government to have some oversight over safety issues re imported products, but the legalization and use of drugs by the people should be decided at the local level. Those states or communities who want them should be able to have them. Those that don't should be able to make them illegal. The federal government should stay out of that. Liberals want the federal government to have total control.
Libertarians take the view that those who want religious symbols, displays, and other religious expression should be free to have them. Those who don't want them should be able to have a socail contract that keeps them out of the public venue. The federal government cannot dictate any matters of religion and has no constitutional authority to interfere with that. Many anti-religious liberals would have the federal government remove all religious evidence from everything.
Libertarians believe people should be allowed to do whatever they choose to be or do so long as it requires no contribution or participation by any others. Liberals do not trust people to make all their own choices and want the federal government to be in charge of much of that.
Liberals want government to be their protector, safety net, mommy, daddy, and available teat if they get into any kind of difficulty. Libertarians see a government that can solve our problems as a government that can and will take anything it wants from us and therefore wants people to work out their own solutions to their problems and deal with the consequences of the choices they make.
Libertarians want the federal government to be restricted to its constitutionally mandated functions and be involved in absolutely nothing else.
I see no similarities of any kind between modern American liberals and libertarians.