Does night takeoff and landing currency also count for daytime currency?
Yes, night landings satisfy the requirements of §61.57(a)(1) for both nighttime and daytime currency.

The wording of the regulation is not crystal clear, and some (including me) have thought that the wording of (a)(2) required daytime landings for daytime currency. This is not the case, per the following interpretation from the FAA (Springfield, IL FSDO, dated 16 April 2014):


  Please note, in this section, there is no mention of a day or night differences in the regulation.
  
  In 14 CFR 61.57(b) the regulation specifically mentions the requirement for Night Takeoffs and Landings and the time period they can be completed in.   If the passenger carrying will be done at night, the additional requirements of 14 CFR 61.57(b) must be met.
  
  The night takeoffs and landings, as required by 14 CFR 61.57(b), will qualify for both the day and night requirement, provided all other requirements are met.   The day takeoffs and landings will NOT qualify for the night (section (b)) requirement though.
  
  Stanley E. Swank II
  Aviation Safety Inspector
  Springfield, IL FSDO, AGL-19


Other sources on the Internet agree with this interpretation:


Eric Gideon at askacfi.com:



  ... your three takeoffs and landings to a full stop at night will also fulfill the recent flight experience requirements for day currency.



A thread at pilotsofamerica.com.