I know that the number in a15 and a19 light bulbs is the maximum diameter of the glass part of the bulb in 1/8 inch increments. However, what I need to know is what is the difference in the bases? Should the a15 and a19 bulbs fit the same socket? Thank You!

They both have a medium base. They both may come in different bases.

Would be nice to know what base your looking for.

They are both medium base bulbs.