How does a differ from c, and b from d?
a. John spotted Bill enter the house.
b. John saw Bill enter the house.
c. John spotted Bill entering the house.
d. John saw Bill entering the house.
I'll preface this by saying that all four are very similar. You asked to compare A with C and B with D, so we'll start with that.
a. John spotted Bill enter the house.
c. John spotted Bill entering the house.
b. John saw Bill enter the house.
d. John saw Bill entering the house.
There isn't much different between the two (enter vs. entering). There is only a slight difference in meaning: seeing someone enter a house sounds more like the action of entering is watched for a short amount of time; seeing someone entering a house sounds like they were being watched for a slightly longer period.
In the end, this is generally a stylistic choice, as the difference between the two is not large enough to cause any confusion for the audience. They are interchangeable.
Now I can go on to talk about the difference between "spotted" and "saw":
a. John spotted Bill enter the house.
b. John saw Bill enter the house.
c. John spotted Bill entering the house.
d. John saw Bill entering the house.
Yet again: very little difference between the two. Spotted implies more often that there was some sort of intent in the action of looking while also implying a quick action (short in time of start to completion), while Saw implies more often just the act of "seeing" and can last for longer.
An exaggerated example: one cannot "spot" a movie for an hour, but one can "see" a movie for an hour.
So with these two bits of information in mind, I would tell you that the most ideal combination of your sentences would be sentence A and sentence D.
a. John spotted Bill enter the house.
d. John saw Bill entering the house.
I should end with a caveat: all four of your sentences make perfect sense! I just suggest these to be the *most* correct.