They have the same basic meaning, but 'liberty' is a bit more poetic, formal and pretentious than 'freedom'. That's why you hear it less than 'freedom'. We have many pairs and sets of words like this in English which are almost synonyms. In general, the one with the Germanic origin (in this case 'freedom') is a more everyday word, whereas the one with the Latin root (in this case 'liberty', which is similar to equivalent words in Portuguese, Spanish,French, and Italian) is the more formal or poetic-sounding one.

They are the same, but freedom is used more in the general sense, Liberty is used more often to refer to a specific freedom. They can both be used to mean a general freedom, though. You can have freedom of movement. (general). You can have freedom from discomfort. (general). You are at liberty to move around the cabin. (Or you are free to move around the cabin). (specific) In the military, "at liberty" means that you are off duty and can go where you want and do what you want.