In simple terms Liberty is usually defined as freedom from excessive government control (Where excessive being the subjective point).
In practice I agree its a bit more nuanced than that.
I'd love to discuss the semantics between these two terms since that seems of interest to you. Lets start by clearly and explicitly stating the definition of interest. Which definition of liberty, preferably from the OED, are we prescribing to here?
https://www.oed.com/dictionary/liberty_n1?tab=meaning_and_use#39406776