What is the difference between a BA15D base, BAY15D (1157) base and BA15S(1156)?

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)

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)

The BA15d base has TWO contacts on the bottom and two parallel lugs on opposing sides of the base 180 degrees apart.

SHOP FOR BA15D BULBS

BA15s (single contact)

The BA15s (1156) base has one contacts on the bottom and two parallel lugs on opposing sides of the base 180 degrees apart.

SHOP FOR BA15S BULBS

for differences between BA15S and BAU15S please click on the link below:
What’s the difference between BA15S and BAU15S Base?