I think you are misguided with the labels "liberal" and conservative.
There are people who want few if any restrictions on freedoms (libertarians). An extreme libertarian is an anarchist. There are people who want many restrictions on freedoms (authortarian). An extreme autortarian is a dictator. But there are many people in between who want some restrictions on freedoms (conservatives, centrists, and liberals). You cannot be both a conservative and an anarchist because conservatives want restrictions and anarchists want no restrictions.
As you said, there are conservative democrats and there are liberal republicans. That isn't a good way to define the parties. People who want some restrictions can be (1) socially liberal and economically liberal, (2) socially liberal and economically conservative, (3) socially conservative and economically liberal, or (4) socially conservative and economically conservative. With four combinations and only two parties, the parties are free to move from spot to spot over time. Republicans tend to be in category 2, 3, or 4. Democrats tend to be in categories 1, 2, or 3. Notice how there is overlap (which is why many libertarians and authortarians claim there is no difference).
Instead, you should look at the type of restrictions to better differentiate the parties. Democrats tend to want personal freedoms and business restrictions. Democrats generally want more drug legalization and the ability to marry anyone of any gender; but democrats want to force businesses to stop polluting or to put gun locks on their products. Republicans tend to want personal restrictions and business freedoms. Republicans generally want the war on drugs and are against gay marriage; but republicans generally want businesses to have few polution controls and the ability to make any gun they want.
This distinction personal vs business restrictions tends to run far deeper than the typical "liberal" or "conservative" labels. Try it on many hot-button issues (abortion, immigration, etc.) They almost always divide themselves into personal freedom / business restriction or personal restriction / business freedom. There are exceptions, but they are far more rare than the exceptions if you call democrats liberal and republicans conservative.