Here is how B3/S23-a4ei6 is different from Life:
Cells in this configuration die despite having three neighbors:
x = 3, y = 3, rule = B3/S23-a4ei6
2o$2o!
Despite having four neighbors, the cells in the centers of these configurations survive to the next generation:
x = 13, y = 3, rule = B3/S23-a4ei6
bo8bobo$3o7b3o$bo!
And all cells with six neighbors survive.
When Golly opens, it runs by default in the last rule it ran before it closed. The rule can be set by going to Control > Set Rule...