To the overall question, "should a house have both a sump pump and ejection pump in the basement?" Well, it shouldn't have either if they're not needed. Ideally you drain by gravity, not with a pump. I've honestly never seen a house with a sewage pump.
That said a weeping tile sump pump should be tied into the storm sewer, whereas a sewage pump should be tied into the sanitary sewer. They should be separate. However, it's not uncommon that the weeping tile discharges into the sanitary sewer. I've heard of lots of them, especially older properties.
Note: not a plumber; I'm a building services engineer, and typically don't work residential jobs.
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