Hey 
You’re comparing the free IEX stream with the SIP data in historical.
Both StockDataStream and StockHistoricalDataClient has a feed argument. If you want quotes from all US exchanges, use the SIP value for the feed (this requires Unlimited Subscription for the stream and for the last 15 minutes in historical). If you want to get IEX quotes, use the IEX value. This means that only quotes from the IEX (v) exchange are included: you can see this in the ask_exchange and bid_exchange fields.
Probably your confusion comes from the fact, that the default value for the feed is IEX for the stream, but SIP for historical (if you don’t query the last 15 minutes).