Grants are just that, resources (usually dollars, but sometimes other resources), given to the recipient who has proposed a course of work that is in accord with a request for proposals or the agenda of an agency. Besides paying for travel or research assistants and M and O, what you are paying is RENT on an ASSET--namely the person, usually the PI, and their accumulated experience and expertise. Presumably they deliver on their proposal, but it is also the case that it may turn out that the original idea does not work so well as another idea. So the grantor in effect decides they wish to encourage someone to deal with a problem the grantor deems important (even if it is proposed by the grantee). and it is not unusual for the grantee to in effect provide much effort than would be expected given the grant's budget. One quarter time in the budget will pay a quarter of salary and benefits, but likely you are getting lots more than you are paying for.
My foundation friends tell me about 1/2 of the grants do not work out, not because the grantee does not deliver, but because the money disappears without a trace, so to speak. So you don't give money to that grantee any longer. Those who deliver, however they find it wise to deliver, are your greatest portfolio asset, for you know that giving money to them will lead to something desirable.
Fellowships are given based on your record and perhaps on your proposed course of work. It would be nice if you produced the book or the articles, but your final report is never checked out. Almost always, people proposed to do much more than they can do. On the other hand, you are wasting your own life if you don't do something that is productive for your work. Over the long run, you are expected to produce that book or those articles, and the fellowship grantor likes to brag about that.
Contracts almost always specify in some detail what is to be delivered, and often that is determined jointly by the grantor and grantee, in cahoots. A precise list of deliverables is a given; a timeline is set. Of course, the list might be revised with the agreement of the grantor. And what you are paying for is the time of the grantor, or perhaps you are paying for the realized deliverables. Time might also be an investment you make to see what someone might do with your problem. Some contracts are in effect a grant or a fellowship, but rarely. Fellowships and grants are never contracts.
Contracting agencies might well ask for specific deliverables after awarding a contract, but it would be much better for them to do so before awarding the contract. As in the overruns on weapons programs, what happens is that the client changes their notion of what is to be delivered, and that means that either the contractee discovers they must work much more than planned without further compensation, or you'll get just what you agreed to when things started up or when the proposed contract was signed on. Or, there will be a demand for further compensation.
Grants buy someone's attention. Contracts buy someone's time. Fellowships are investments in the scholarly infrastructure. Usually, the grantor received twice what it pays for. BUT, contractors cannot afford such generosity. But the contracting organization gets what it believes it really needs. In general, grants and fellowships get you much more than you paid for, contracts perhaps a bit less. Grants and fellowships buy you someone's commitment, contracts buy you someone's product (a product that will fulfil the contract but is likely to be satisficing).
Grants are often in the realm of philanthropic activity. Fellowships are too. Contracts are in the realm of commerce and mercenaries (often not war-fighters). In a contract you'll get what you paid for, but in a grant it is up to the grantee to figure out what is the best outcome of the research.