There are many senses in which political philosophers down the years have used the words 'freedom' and 'liberty'. Some of these can be ignored - for example, Hegel's use of the word (roughly, "acting in accordance with reason,") seems rather abusive of the intuitive meaning we attach to it - but there are at least three meanings worth considering.
First, Negative Liberty, or the absence of oppression. If someone threatens to hurt you if you carry out an action of which they disapprove, they are violating your negative liberty.
Second, Positive Liberty, which is somewhat vague but refers to a general idea of autonomy and self-mastery. The key difference with Negative Liberty is that anything can count as a restraint on your liberty - while Negative Liberty focuses upon limitations emanating from other agents, Positive Liberty considers physical impossibility, absence of necessary materials, even lack of self-control.
As a side note, I do not personally think about either of these (at least directly) in terms of my value judgements, I tend to think more in terms of the inherent wrongness of imposing your will upon another person. Of course, then I have to explain precisely why I think that this is wrong, so I probably do attach some value to freedom.
These are the two main ones. The distinction was introduced by Isaiah Berlin in his speech "Two Concepts of Liberty" and there is a notable debate over which of the two better reflects the meaning we attach to the words 'freedom' and 'liberty'. However, there is also a third way in which the words may be used - that is, "Freedom as Non-domination" or "Republican Freedom", roughly defined as the absence of being subject to arbitrary power - the emphasis of that being on the word 'arbitrary'.
On the way back from The Great Escape, I listened to a podcast in which Philip Pettit was interviewed about a book he had written defending this interpretation of liberty. He made reference to a play by Henrik Ibsen - I can't remember which, but it was most likely A Doll's House - in which there is a woman, subject to a man (her husband?) who dotes upon her and will give her whatever she wants, but also holds complete power over her. He argued that she was not truly "free" because of the fact that her apparent freedom was entirely reliant upon the will of the man.
I personally find this unconvincing. I would say that she is free, and that perhaps there is an X such that we value X, X corresponds to non-domination, and we don't actually value freedom. This seems rather closer to the actual political and philosophical issue than merely arguing over precisely what we intuitively mean by "Freedom". As a somewhat rough analogy, we have distinct concepts of 'total utility', 'average utility', 'eudaemonia', and 'preference satisfaction'. When arguing about what is valuable, we do not argue about which of these is somehow a more authentic representation of what our intuitions conjure up when presented with phrases like 'utopia' and 'the good life' but instead argue about which is actually more valuable.
A second distinction in types of freedom: I shall refer to "metaphysical" freedom and "political freedom". By political freedom I mean the stuff I have just been talking about - a general notion of "not being enslaved". By metaphysical freedom I mean freedom of the will. I believe there to be a tendency for people to confuse the two - I don't blame them, most people are not trained to be absolutely clear in their language, there are several other words which can mean more than one thing (e.g. Libertarian and Libertarian).
In particular, there is one confusion which I have only just understood. The Bible often promises that we may have freedom through Christ. It is easy to see how this may be understood as political slavery - we were slaves to sin and death, but now are no longer subject to judgement.
Except that we don't become fully autonomous agents: we become servants of God. I'm not denying that this is an improvement in our condition (see, again with the "it's not precisely freedom which is valuable"!) but it doesn't really seem like an increase in our freedom. We go from one master to another master - a better master, to be sure, but at no point do we cease to be owned in some sense.
But take this passage, Romans 7:15-25 (taken from the NIV):
Now it becomes clear that the freedom we achieve through Christ is metaphysical: we are unable to control ourselves and to avoid sin due to our sinful natures, but due to his intervention we are not controlled by sin and can do what we desire - that is, to love and worship our Lord God.15 I do not understand what I do. For what I want to do I do not do, but what I hate I do. 16 And if I do what I do not want to do, I agree that the law is good. 17 As it is, it is no longer I myself who do it, but it is sin living in me. 18 For I know that good itself does not dwell in me, that is, in my sinful nature.[a] For I have the desire to do what is good, but I cannot carry it out. 19 For I do not do the good I want to do, but the evil I do not want to do—this I keep on doing. 20 Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.21 So I find this law at work: Although I want to do good, evil is right there with me. 22 For in my inner being I delight in God’s law; 23 but I see another law at work in me, waging war against the law of my mind and making me a prisoner of the law of sin at work within me. 24 What a wretched man I am! Who will rescue me from this body that is subject to death? 25 Thanks be to God, who delivers me through Jesus Christ our Lord!So then, I myself in my mind am a slave to God’s law, but in my sinful nature[b] a slave to the law of sin.