They are Army Sqns as well with the 6 being the block, the second number being recce or attack and the last, the Regt so - 663 would be recce of 3 Regt and 653 would be attack of 3 regt.
661, 662, 663 and 664 Squadrons go back a lot further than that. No 660 Squadron was formed in Aug 1943, No 661 Squadron was formed also in August 1943, No 662 Squadron formed Sept 1943, No 663 (Polish) Squadron formed Sept 1944 in Italy and No 664 Squadron R.C.A.F. formed Dec 1944. All were formed for Air Observation (AOP) duties with Auster aircraft. Following the end of WWII many were disbanded and reformed as Flights. In 1957 when the Army Air Corps (AAC) was born a number of the Squadrons were reformed and became AAC Squadrons. In the mid 1970 action was taken to implement “New Horizon” establishments proposed under a Defence Review which saw the reorganisation of the Army Air Corps in BAOR under a Regimental basis with each Regiment having 2 Sqns thus 1 Regt consisted of 651 and 661 Sqns, 2 Regt - 652 and 662 Sqns, 3 Regt - 653 and 663 and 4 Regt 654 amd 664 Sqns with 9 Regt - 659 and 669 Sqns.