I had a fridge that I moved out of the way exposing another section of my brick wall, but there is a noticeable difference between the newly exposed brick and the rest. I'm not sure what this stuff is on the surface & how to get rid of it. Any help would be much appreciated.
That brick wall has a lot of character!
Cleaning brick can be messy, so have plenty of old towels on hand or use some drop cloths. I would suggest cleaning all of the brick with a hard bristled brush. Use either a mixture of soap, vinegar and water or you can clean it with a solution of muriatic acid and water.
If you go the acid route, be sure to wear gloves and eye protection. Follow mixing directions on the acid container carefully. Also, be sure to ventilate the area well.
Either way, be sure to rinse the surface with plain water. You can do the cleaning in small sections and when you rinse, dab it with a thick towel.
If you want to bring a natural uniform look back to the brick, allow the surface to dry and apply a uniform coat of Brick Sealer. Sealer will bring out the original color of the brick and give it a nice shine. The sealer is also available in a low-luster version.
I had a customer use corn cob media in a sandblaster to get all foreign material off without disfigurement of the brick and morter. The room needs to be masked off and it takes a lot of media per square foot but the end result is a beautiful wall. Different sand blast media gives different results.
It is likely that the area of the room where the refrigerator was not protecting the wall has attained the darker color due to the bricks being exposed to air flow including air that carried dust and even oils from cooking in the kitchen.
It really does look to me that the newly exposed area is the more "uncontaminated" surface. It may be possible to attempt to clean the original brick faces with a good scrub brush and hot soapy water. You may be tempted to think that a pressure washer may make that cleaning job easier but, besides the huge mess that would make, it does not look like the ancient brick work could stand up to that, especially much of the questionable mortar joints.
Some of that might be due to natural oxidizing of the exposed bricks due to exposure to UV in sunlight from the windows and when the fridge was there, it blocked that UV light. So one option is that you could leave it alone and see if the newly exposed brick "catches up" to the old stuff in terms of the oxidization. It might be that in 6 months you will not notice it any more.