Not quite.
Players receive a one-match ban for (a) two yellow cards, (b) a straight red card awarded for denying a goalscoring opportunity by physical means or by handling (Robbie Keane against Bolton on 25 February, for example).
Players receive a two-match ban for a straight red card awarded for offensive, insulting or abusive language or gestures.
Players receive a three-match ban for a straight red card awarded for violent conduct, serious foul play or spitting.
Where a player is suspended multiple times in the same season, an additional one-match ban is served for each subsequent suspension. For example, a player dismissed for violent conduct and suspended for a third time in the season would serve a five-match ban.
Source:
The FA Handbook 2006-2007, pp. 202-203