Brighteners - need to be the same as cleaner brand?

So much GREAT info on this site - can't find this question answered.

Do you need to use brightener from same brand as cleaner or can you mix and match?   I can buy Thompson Oxy Foaming Action cleaner locally but they don't seem to have a brightener.   Wolman seems to have Deckbrite and a brightener and also a two in one product (DECK & FENCE BRIGHTNER WOOD CLEANER & COATING PREP)  that I've seen you recommend staying away from (not specifically Wolman - but two in one products in general). 

So my specific question is:  can I use the Thompson cleaner and the Defy brightener?

Thanks much!