www.alphadictionary.com

I was thinking of these words in the context of hoping for a good outcome. "I was sorry to hear about Paul's diagnosis; tell your husband that I am pulling for him".

They are both simple words, but often simple words have amazing power.

Simple words also often have the most definitions and variations in meaning. Seemingly far apart, I can see how these came to have the meaning of encouragement.

According to etymonline, root's version came first, with pull following along a decade or so later.