Which animatronic is "Fred Bear"?

There is no "Fred bear."

Certain YouTubers and bloggers use this as a nickname. It usually refers to "Freddy."

When people talk about, they refer to one of the first anamatronics in the original Fredbear's Family Diner which is a predecessor to Freddy Fazbear.

While it's theorized he is Golden Freddy due to his appearance of golden and purple bowtie it's not 100% confirmed either way. In FNAF4 he does appears in nightmare form on night 5 and is seen in the 8-bit minigames between nights in FNAF4 and the Stage01 minigame in FNAF3.

Fred bear is possibly golden Freddy. Some of us believe that Scott Cawthon will explain in Fnaf sister location 2 (Fnaf 6). I may be wrong but if you play the first Fnaf and try custom nights, put in the animatronics order 1 9 8 7 and golden Freddy will appear. In the same look as Fred bear. If you try this then be careful because if you let golden Freddy's jumpscare end then you go all the way back to night 1. Another way to see golden Freddy is (really rare) he appears under the poster of Freddy (still Fnaf 1) then under the desk. Again he will jumpscare you and crash your game but there is no way to make that happen on your own accord.