I'm trying to get a handle on how much I'm eating so I'm using a food journal. Is 4 oz the same as .5 cup?

Excellent question! No, it's not. If you look at a bag of lettuce mix at the market, you'll note the weight is around 12 oz -- yet contains 12 cups! Clearly 12 oz for a huge bag is way more than 1.5 measured cups.  A large 6 oz chicken breast is not the same as 3/4 cup (6 oz) measured.

The general rule when you're tracking food is to measure animal protein (fish, chicken, beef) by weight on a food scale and measure everything else by volume in a measuring cup.