When someone asks you "to commit" to something, there are two interestingly different senses of the word to consider and disambiguate. The first is a synonym of "dedicate" - to be committed to something is to be dedicated to that thing. To care, to value, to be devoted to that object. The other sense is a synonym of "bind" - to be contracted in a way that restricts freedom of future action. To make a (sometimes legally binding) promise about the behavior of our future self based upon the word of our current self.
Today I'm feeling the very different textures I get from those two senses. The former is care and expression, the latter is obligation and security. They could be said to have the same net effect with respect to how other people feel: reassurance and confidence in their ability to rely on something about one's future behavior. Maybe it's only the level of specificity that varies, from the vague "I'm committed to this value/cause" to the concrete "I commit to do thing X at time Y". But the difference in texture that I noticed - I think that points at power and freedom.
If a feeling of commitment is sought, then the other is looking for better understanding of your current state. If a binding commitment is sought, then the other is looking for confidence of your future behavior regardless of your future state. There's a (or an implied) difference in trust there - which is probably why some people actively prefer vague handshake deals to formal contracts. They value the trust, want to signal their trust as they extend trust, and don't value the contractual binding as much.
I'm going to shift my wordage slightly from commitment to agreement now. I feel a marked preference for the latter, and think it's because calling something an "agreement" specifies the first texture of "commitment" while avoiding the second. The word connotes more mutuality to me, and also implies a different power relationship. Agreements are made between two (or more) parties, whereas a commitment is more often one-sided.
There's nothing firm in the definition of those two words that forces this, but I would use "commitment" when there's some sort of penalty for failing to honor the obligation, and "agreement" when more future freedom of the agreers is preserved. The goodness of agreements comes from the understanding, and not from the binding, is the way I'm thinking of it. To agree on a plan is to bring clarity - to commit to a plan is coercion of our future selves. When the world changes in the future, is one "committed" to the old plan? The same way in which one is "committed" to a mental hospital? There's the force laying underneath that word.
The best agreements, in my humble opinion of course, are ones that preserve the sovereignty of the individuals making them. They record the values and intentions of those people at that moment, and making them explicit and clear is a very helpful thing. But "you committed!" is a tool of force, while "you agreed!" leaves more room to recognize the agency of the subject. Whether diverging from that agreement-or-commitment feels like a shameful betrayal or a completely sensible adaptation mostly depends upon the degree to which it had attempted to remove the power of that person's future agency.
Great agreements can be made without taking away agency or power from any people. The best relationships are made up of continuous dedication, moment after moment, not sustained by the force of a prior binding. A marriage that is held together only by law is already dead. A joint venture held together by contractual obligations is doomed to defection. Skillful agreements should recognize this and focus on the present. Specify what's important to understand, and specify how to communicate and modify the understanding when things change in the future. Living agreements, modified and/or renewed frequently, reflect a healthy relationship more than a past commitment.
Are there appropriate times for the force of contracts? Absolutely. But think of the classic advice around commitment in romantic relationships. Someone wanting their partner "to commit to them" is better served by letting them go free, having already lost the trust and understanding that grounds healthy relationships. (Marriage shifting from mostly-contractual to mostly-relational over the course of centuries probably accounts from some of our conceptual muck here.) Of course, healthy relationships should still have a multitude of agreements about e.g. who's doing the dishes. Those aren't about binding, but about relating and understanding - which are what healthy relationships are about in the first place.