On five-speed auto transmission with S/W selections, you are certainly right: S is for Standard and W is for Winter.

At S all five-speeds will start at first gear from standing still.

At W the story differs a little:

On 4-cylinder models and some low displacement 6 cylinder models, it will start at second gear.

On high displacement 6 cyliinder models, all V8s and the V 12, it will start on third gear.

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A. Rosich
CL 500, 1998
S 500 L, 1998
E 320 T, 1995 [Sadly sold ]