B737-800
Flight Crew Last 90 Days 155; Flight Crew Type 11000
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Human Factors
We were near KIKKR on the GIBBZ 2 Arrival and cleared direct MOSBY. We misheard the clearance and proceeded to MOSLE.  Shortly after; the Controller asked if we were still on the arrival and we said yes.  He said no problem that happens here and he meant for us to proceed to MOSBY on the approach to Runway 1R; he then gave us a vector. Either MOSLE or MOSBY needs to be renamed they are too similar in spelling and sound.
B737-800 Captain on the GIBBZ2 arrival to IAD; reports confusing their clearance direct MOSBY as direct MOSLE; and believes they are too similar to be in the same airspace.