You have a Black Edition FX processor. Yours is just binned in the average range for an average overclock with the FX 6300. People like to incorrectly say things about FX processors all the time like "the FX 6300 and the FX 6350 are the same processor, one is just factory clocked better"and "there is no difference between the FX 8320, FX 8350, FX 8370 or FX 9xxx series they just have different factory stocks" (and in the case of the FX 9xxx series different TDP). These people are wrong, yet their opinion perpetuates throughout these pages and other tech sites.
The FX 6300 and FX 6350 do not have the same binning. The FX 6350 chips have better binning and can therefore overclock better than the FX 6300. Now it is true that earlier chips were not all that different and in a lot of cases an early FX 6300 would have the same binning, sometimes better than the FX 6350. However the Piledriver arch is in a very mature stage at this point and the chips are separated not by clock speed but by binning. The FX 6350 has better binning than the FX 6300. The same is true of the 8 core processors the FX 8320 has the lowest binning, the FX 8350 has mid-range binning and the FX 8370 and FX 9xxx series have the best binning. I haven't overclocked a newer FX 8320 that was able to get stable over 4.6Ghz in a very long time, however early samples could overclock to 5Ghz. The FX 8350 usually hits the wall at the 4.8Ghz range now, current chips are very lucky if they can get to 5Ghz (early samples could get over 5Ghz). The big overclocker is now the FX 8370, which on average can get to 5Ghz, and better samples can get more than 5Ghz. If overclocked properly the FX 9xxx series can also overclock nicely (although you really have to know what you are doing with these 220W beasts).
The point is the FX Piledriver process is very mature now and you get what you pay for. The lower tier processors will run great at stock, they can all still overclock, but will never overclock as well as the upper tiers anymore. Overclocking is all dependent on the binning of the chip and the higher tier processors have the best binning.
Looking at the screen shots of your overclock it is a safe bet that at your 4.5Ghz overclock it would not pass Prime 95 or OCCT for a 4 hour run, so its not going to be stable at 4.5Ghz. Your best overclock that you can achieve with your FX 6300 is 4.4Ghz, and there is nothing wrong with that. You are 900Mhz over your stock clock and should get a nice bump in performance. I would say for current FX 6300 processors you are right in the normal range for what you can hope to get out of an overclock with the FX 6300, 4.4Ghz is nothing to be "ashamed" of.