You apparently are using the Morningstar calculator for a TS-45. This is a different controller than a TS-MPPT-45. You will get very different results. If you're going to use the "24v" panel and a 12v battery you need the MPPT version.
By the way, the terminology is pretty consistent in the industry. There's just a lot to this. I work for a solar company. I install this stuff every day. We employ engineers who design these systems all day. I've got multiple licences and certifications to install things.
After you take amps, watts, volts, (both input and output), battery size, temperature, tilt angle, azimuth, etc. into account it does get complicated. We also have to deal with meeting the National Electric Code that gets changed and re-written every 3 years. Don't feel bad that you can't figure this out online in a few hours.
