What is the difference between an agreement and an undertaking?

From a purely definitional standpoint, Black's defines an undertaking as either a "promise, pledge, or engagement" or it can also be used to refer, specifically, to a bail bond. An agreement however, has contractual overtones and is generally defined as "a mutual understanding between two or more persons about their relative rights and duties regarding past or future performances" and tends to require the elements of contract (offer / acceptance / consideration).

In practical terms, an agreement requires that both parties actually 'agree' to do something or exchange something (e.g. documents, money, etc.) while an undertaking is generally a unilateral promise by one party to do something within the context of a course of negotiation or transactions (e.g. one party to a dispute "undertaking" to produce certain documents in dispute).

Both can be enforced but the manner of enforcement differs slightly. An agreement may be sued over in contractual terms (need to prove offer / acceptance / consideration / detrimental reliance) where one party detrimentally relies whereas a breached undertaking can be sued for under elements of detrimental reliance on a promise (need to prove the promise and reasonable, detrimental reliance).