Hi,
There are several options of the UPS plugin which can change the rates calculated by UPS besides the warehouse information:
The pickup type, the destination type, the negotiated rates, the include prices, the exclude dimensions and the group packages option can all generate a different price.
From your screenshot of the UPS calculator, it seems that you selected a different pickup type than what you have configured in the plugin. And you configured a "commercial desitination" in the UPS calculator but not in the UPS plugin.
The rates are given back by UPS themselves. If they say it should be $23.22, it means that with the way the plugin is configured that's this price which should be paid. If you see a difference in the calculator, it means that something is different in your plugin settings and in the calculator settings. If you have trouble with the settings, I would recommend to contact UPS for help to understand what options should be used to get the same result, they know better than us their calculator settings.