"Hopefully one of our nautical experts will be more adept at answering the question of whether the white uniform was actually onsidered "formal" and the blue "informal."
If I may pretentiously join the 'nautical experts' just this once....
I am not familiar with the footage you refer to but I would surmise it depicts Captain Smith wearing No.10's - formal tropical day dress (there later developed the less formal shirt, shorts and white knee socks day dress but this was not universal in passenger vessels, for instance the catering officers would keep to No.10's). The designation 'No.10' is a spillover from the Royal Navy dress code.
Depending upon either zone or prevailing weather the prescribed dress code handed down from the bridge was either 'whites' or 'blues'.
'Whites' on the UK coast in April would be unthinkable. Uniform gloves with 'blues' would be black leather. While the north Atlantic is never a tropical run, New York in high summer with its attendant high humidity would almost certainly warrant 'whites'.
Evening mess dress mirrored the prevailing day dress except that 'blue' mess jackets in later decades became almost universally superseded by 'white'. Either way, mess jackets were worn with bow ties, cummerbunds and barathea trousers with 'lighting conductor' stripes.