I have been the 'Clan' Archivist for FLOYD and FLOOD for several years now and have built up a large amount of data on both family groups.
As Willy says, most FLOYD families probably arose as a corruption of the Welsh LLOYD (= grey), as pronounced by non-Welsh speakers (surnames were mostly phonetic for hundreds of years before they were written down). However, I don't think that most FLOOD families were ever FLOYDs (or vice versa).I believe that the FLOODs arose independently in several areas from the connection with low-lying areas near rivers.There was also the Irish connection where the various forms of TULLY were translated into the English FLOOD as political expediency demanded from time to time. Having said that, I know of a few instances where FLOOD has become changed to FLOYD, my own family included, generally in branches which moved away from their own native area. The reverse alteration (FLOYD -> FLOOD) is not so common.
I have done a distribution analysis for both FLOYD and FLOOD (and FLUDE etc) in the 1881 Census for Great Britain (Scotland, England and Wales, but not Ireland) which shows that, apart from the major cities,the two families have little in common, location-wise.
There are 3167 FLOOD group individuals in the 1881 Census, with the major clusters being Lancashire (505)(the Irish connection), Middlesex (=London) (407), Devon (185), Kent (180), Surrey (149) and Norfolk (143). There is also a highly significant cluster of FLUDEs (148) in Leicestershire
There are 3106 FLOYD group individuals in the 1881 Census, with the major clusters being Middlesex (427), Cornwall (222), Warwickshire (=Birmingham)(202), Lancashire (187), and Surrey (178).The most distinct of the clusters is Cornwall, where they are almost all in the extreme south-west tip of the county and associated with the copper/tin mining industry. There are also 129 FLOYDs in Glamorgan (Wales).
In England the numbers of FLOODs and FLOYDs are about even (1:1) whereas in Scotland the FLOODs outnumber the FLOYDs by about 3:1 and in Wales the FLOYDs outnumber the FLOODS by about 2:1.
(Source: FLOOD-FLOYD FAMILY ARKive, No.1, Feb 1997).
Jim Floyd (Guild of One-name Studies representative for FLOOD and FLOYD)