When I hear liberal, I think of someone that is socially progressive and promotes an economic security net. While they also promote a progressive tax system, they are generally okay with capitalism and private ownership of the means of production (people can own how things are made).

When I hear leftist, I think of someone that would like to revolutionize the economic system so that wealth is distributed more equally by changing our economic relationships. Typically, this includes the abolishing private ownership of the production of means. They also tend to be more progressive with social matters, though there is variability between the different leftist perspectives. Beyond that, things get complicated. You could have leftists that argue for a strong centralized economy to a loose federation of workers unions and no state whatsoever.

Basically, liberals argue that we can make capitalism work better with progressive reforms. Leftists argue that the economic system needs to change entirely, with a focus on who controls the way we produce things, especially requirements to live (e.g. food, housing, energy, etc.).

It's important to understand that political identity is fluid, meaning people can change their minds as they learn new information and hear different perspectives. Individuals are not constrained to a political identity. In fact, the political identity is a shorthand that communicates the political perspectives efficiently.