Are you a pilot flying these machines, or any other aircraft, or a flight simmer?
Indeed, considering the first quote, that is a very valid question...
However, the answer is found in Aircraft Limitations. We just got a complete revision of the wind section, now there is a difference between take off and landing whereas before both were identical. All wind limits now include gusts, so the highest windspeed reported is limiting. However that is a company tailored manual so differences to a standard boeing FCOM are possible.
Crosswind limits for takeoff (B737-700/800):
Dry (with winglets) 34 kts
Dry (without winglets) 36 kts
Wet: 25 kts
Standing Water / Slush: 15 kts
Snow - No Melting: 25 kts
Ice - No Melting 15 kts
Crosswind Limits for landing:
Dry: 40 kts
Wet: 40 kts
Standing Water /Slush 20 kts
Snow - no melting: 35 kts
Ice - no melting: 17 kts.
Crosswind Limits for autoland: 25 kts.
Crosswind Limits for autoland (One Engine Inoperative): 20 kts.
Crosswind limit have to be reduced by 5 kts whenever assymetrical thrust is used, sideslip only (no crab) landings are not recommended with crosswind components greater than 17 kts at F15, 20 kts at F30 or 23 kts at F40. Take off and landing on untreated snow or ice is only allowed if no melting is present.
All limits are valid for both narrow runway operation and runways with a width of 45m or more.