David Jones is described as formerly such "Minister for Brexit". But how is this job description related to the position of Brexit Secretary which was (only) held by David Davis and is now held by Dominic Raab?
"Minister for Brexit" is a more general description of high-level positions in the Department for Exiting the European Union (DExEU). The Department is overseen by the Brexit Secretary (currently Raab), who himself counts as a "Minister for Brexit" (assuming Wikipedia is correct on this.)
There are two other positions that also count as a "Minister for Brexit":
Minister of State for Exiting the European Union (currently held by Rt Hon. Lord Callanan)
Parliamentary Under-Secretary of State for Exiting the European Union; with three MPs serving in this role currently.
More generally, a Minister of State is a more junior position in the British government, usually reporting to a Secretary.