Not just guns
In the United States, liberals believe in higher taxes and spending on social priorities. Conservatives want lower taxes and social spending.
In campaign finance in the US, liberals want restrictions to how much campaigns can raise from individuals. Conservatives are against restrictions.
Even in areas like gay rights, the freedom/restrictions dichotomy is not as clear as you make it out to be. Take the cake baking issue. You can view this as absolute freedom for people to buy cakes saying anything they want anywhere they want. Or you can view it as a removal of religious freedom and freedom of speech from those who disagree. How you view it probably depends on which freedoms you find more important: gay rights or religious rights.
Words changing meaning
The obvious definition of liberal (from Dictionary.com) is:
favoring or permitting freedom of action, especially with respect to matters of personal belief or expression
But note that that is the fifth definition. Contrast with
of, pertaining to, based on, or advocating liberalism, especially the freedom of the individual and governmental guarantees of individual rights and liberties.
But those principles contradict each other. If the government guarantees individual rights and liberties, it has to restrict the freedom of the individual to do so.
Gun control is an attempt by the government to guarantee the right of an individual not to be shot by a gun. But it operates by restricting individuals from owning and using guns. Where it is most successful it does so rather extremely.
For example, in Japan, just carrying a gun or a bullet is illegal without a special permit which is very difficult to get. And more importantly, in Japan, there is no exclusionary rule. Any successful search is a good search and can be used in evidence. So the police do not have to show probable cause. This makes finding illicit guns (or bullets) easier. Japan is so successful at this that not even the police carry guns.
Is Japan a police state? Many thinks so. Does that make it liberal or conservative in your book?
Democrats are liberal and left-wing. Republicans are conservative and right-wing. So we make the words match the actual ideologies as practiced rather than intellectual definitions.
In the US, Democrats are primarily an urban party while Republicans are a rural and suburban party. Republicans have next to no representation in urban areas. Democrats have better representation in rural and especially suburban areas.
In urban areas, there are large police forces and active police who are not far away. Firing a gun tends to be illegal because bullets can travel through walls and hit others. People are more worried about bullets that miss their target and hit someone uninvolved. Such people value gun free zones.
Rural areas tend to include hunters and people who are less worried about being attacked by guns and more worried about invasion of their home. Such people value easy access to guns.
Suburban areas are something of a compromise. They have fewer problems with crime in general. But they have higher density and more risk to firing guns. Many suburbs were formerly rural areas. Long time residents may think more rurally. Newer residents may have moved from urban areas to get more room and raise a family. For that matter, some suburbs are actually quite urban, only separated from adjacent cities by arbitrary borders.
Gun freedoms are more of a rural issue than an urban issue. Gun control is more of an urban concern than a rural concern. So the group that finds gun control important is the urban, liberal group. While the group that finds gun freedoms important is the rural, conservative group.
You can see the same pattern in gay rights. The urban, liberal group values the rights of gay people to do things more than they value the rights of religious people to not do things. Thus, they favor positively forcing people to write messages with which they disagree on cakes. The rural conservatives value their religious rights and freedoms more.
The truth is that most people are not that ideological. Instead of constructing intellectual justifications, most people make political decisions emotionally. Urban people are more worried about being shot by criminals than losing the guns they mostly don't own. Rural people are more concerned about losing guns they do own than rare instances of crime committed with them.
Any ideological explanation tends to come after those decisions are made. First there is an emotional reaction. Then there is a rationalization.