FWIW, according to Christoper Leahy in "The Birdwatcher's Companion to North American Birdlife" :
"BEAK : Essentially synonymous with BILL. In more restrictive usage, refers particularly to larger bills, especially the hooked beaks (or bills) of birds of prey. In general `bill' is the preferred term in ornithological/birdwatching contexts."
Stuart- there was an earlier thread on this but I can't find it. For questions like this I refer to my trusty and trusted "New Dictionary of Birds" written by Sir Arthur Landsborough Thomson, published by Nelson in 1964. The entry for "Beak" is short and sweet: "synonymous with bill". The entry for "Bill" is considerably longer:
"alternatively 'beak' and technically 'rostrum', the projecting jaws of a bird, with their horny sheaths. The whole consists of the upper mandible (or maxilla) and the lower mandible; the former is based on the facial bones, especially the premaxillae, and the latter on the composite jaw-bones. The horny coverings of both are formed by the outer layers of the Malpighian cells of the epidermis. The whole horny structure is known as the rhamphotheca, the upper and lower portions being sometimes separately designated rhinotheca and gnathotheca".
Having quoted Landsborough Thomson who is definitive on the subject, I agree with Steve and others that each word does have a connotation, however, vague. I don't think many people would refer to a duck's beak, or an eagle's bill.
A wonderful bird is the Pelican
His bill will hold more than his belly can
He can take in his beak enough food for a week
And I'll be darned if I know how the HE**ican.