One is descriptive, from the Old Scots and Old English reid meaning "red" and describing someone with red hair or a ruddy complexion. The other is locational, from the Old English riedmeaning a clearing and describing someone who lived in a woodland clearing. There are also various place-names called Reed, Read or Rede with different derivations.
The Reid spelling is mainly Scottish. Reid numbers are also high in Northern Ireland and in Canada, reflecting probable Scottish immigration there. Read is the main spelling in America.
Since it means Red, then Blood has long been associated with Red as a colour.