Hi Eagle90,
Sure hope I'm not confusing the issue but - looking at your second picture it seems to me that the compressor output is male 1/8" BSP (my HF clone is) and the Aztec hose is female 1/4" NPT so you need an adapter that will allow connecting your Aztec hose to the compressor ( the other end already fits the Aztec AB - right?). Good luck finding that it a local hardware store (at least in my small town with only Lowes and Home Depot). You can get one from AMAZON but you have have to buy $25 worth of stuff for them to ship it. My suggestion: If you have a Harbor Freight nearby, buy one of their AB hoses (blue braided and <$8) - it willl fit your compressor or buy TCP Global hose and an Aztec AB to Master hose adapter, both from TCP Global and you'll be set. Yeah, more waiting, I know. But by doing it this way, if you ever decide to buy a Master, Iwata, Harder & Steenbeck, Grex or most other ABs you'll be set. Badger, Paasche and Aztec are the only ones I know who don't use 1/8" BSP threads on their AB's.
PS Be aware that 1/8" NPT or NPS (which might be available locally) don't mate with 1/8" BSP. 1/8" BSP (correctly , BSPP is 28 threads per inch) and NPT or NPS is 27 threads per inch. BSPP is British Standard Pipe Parallel (there is also a BSPT - British Standard Pipe Tapered) and NPT is National Pipe Tapered or NPS , National Pipe Straight but the TPI is different between British and Imperial standards. Most AB specific compressors use 1/8" BSPP output though 1/4" NPT is common on shop size compressors in the US.