One question I have is... I've been shooting in RAW and taking the photo and increasing and decreasing the exposure and saving various photos. Is there much difference in doing this vs taking multiple photos changing the exposure on the camera?
Yes, there is a slight difference, doing what you say, you did no hdr at all

you only got a different render of your RAW data.
HDR is about trying to solve the problem of too high dynamic luminosity. The dynamic is limited by many bottleneck, file format (8 bits colour depth in jpg), camera sensor (10-12b), display, graphic cards, prints and your eyes.
How many shots you need to capture the scene dynamic depends on the scene by itself. What you show us does not seem to need more than the 8b/c limitation (just look at the histogram). If you are attempting to shot with direct sun in the frame, you will need many shots, with massive underexposure to get the highlight and some overexposed to get the shadow zones.
HDR file format (floating point representation) will solve first point, taking several shots with different exposures, will solve the second one. Tone compression and tone mapping is a workaround for remaining points.
Please, do not hesitate to correct my English, especially technical terms.