Compare Different Bayonet based part no. 1156, 1157, 1142, 47386, 7507
Bayonet based abbreviation is BA followed by a number, which represent the base diameter in mm.
BA15 base is a Bayonet base with a diameter of 15mm (0.59in), Buy Tail/Brake LED bulbs for cars
The lower case after the base diameter represent the number of contact on the bottom of the base, and based on the number of contacts there are 2 base types: 
d - double contact
s - Single contact


BA15d (double contact), Part no. 1142
The BA15d base has TWO contacts on the bottom and two parallel lugs on opposing sides of the base 180 degrees apart.  Dual Contact Bayonet DC Marine.

BA15s (single contact), Part no. 1156, Single Contact Bayonet
The BA15s (1156) base has one contacts on the bottom and two parallel lugs on opposing sides of the base 180 degrees apart.

BAY15D PREFOCUS double contact bayonet base, Part no. 1157
When one of the two parallel lugs is higher than the other one the base is named BAY15D (1157) PREFOCUS double contact bayonet base, DC Marine

BAZ15d P21/4W dual contact bayonet Offset pins, Part no. 47386 
Bayonet base with a diameter of 15mm (0.56in) with a dual contact on the bottom of the base, It has two lugs on the side of the base and has the lugs at 150 degree apart.

BAU15S 7507 PY21W
The BA15S and BAU15S are both Bayonet base with a diameter of 15mm (0.56in) with a single contact on the bottom of the base, BA15S (1156) vs BAU15S (7507 PY21W) base While both bases have two lugs on the side of the base the difference between them is that BA15s have the lugs at 180 degree and BAU15s has the lugs at 150 degree apart.