Well the Brown Widow is typically light brown tanish color with an orange hourglass instead of a red one. But they are often misidentified because the Western Black Widow, in it's not mature stage still developing, appears very similar to the Brown Widow. The main identification would be on the stripe down the middle of abdomen, on the back.
The Black Widow stripe is much more defined. So the other way you can identify the Brown Widow, is on the egg sac versus the Black Widow egg sac. The Brown Widow egg sac has little spiky things on it kinda like a medieval mace. Where as the Black Widow egg sac is very smooth and very silky. If you happen to see the egg sacs that's how you would know.