CHECKIDENT(RESEED) is quirky, based on TRUNCATE/DELETE & whether the table is a brand-new (never-contained-any-rows) table or an already-existing table.
CHECKIDENT(RESEED,0) acts differently, based on the above. If it's a brand-new table, then, yes, it will start the key count at key = 0 (1st actually assigned key will be 0.) However, if it's an existing table that's been deleted from (not truncated), it will actually start the key count at key = 1 (1st actually assigned key will be 1.)
I need to delete from (not truncate) the table, due to foreign keys. So, the 2nd example (CHECKIDENT(RESEED,0)) restarts my keycount at 1.