Differences:
The main technologies for 3g are CDMA (Verizon/Sprint) and GSM (AT&T/T-Mobile). Here in the US, where I am based so that is the easiest information for me to get and where I focus on, the major technology is CDMA. While the world has adopted GSM for the main technology. Along with 4G technologies, 3G technologies are NOT compatible. You CANNOT use a CDMA phone on a GSM network and vice versa.
The main technologies for 4G are LTE and WiMax. In the early days of 4G, the technologies were more based on region than company or network. WiMax was based in the South, East/West, while LTE was base more in the Northern areas, but neither technologies really made it into the main cities before they were adopted by the cell phone network companies. Fortunately for us in the US, both the US and the world at large seem to be looking at LTE as the standard (although there are still countries with WiMax as the standard) since the WiMax crash we saw a few years ago.
Similarities:
Both 3G and 4G networks allow access to the Internet, although most of the differences I have see are under-the-hood. The biggest difference that I have seen is that load times of webpages are quicker. If you haven't been reading up, the networks are running out of bandwidth and the FCC has been very reluctant to give them more. This is not like cable companies where you can just build more cable lines, there is a finite amount of room each company gets on the electromagnetic spectrum (light spectrum). Both 4G technologies are better at compressing data than both 3G technologies. Unfortunately, the demand for bandwidth is growing exponentially so we could very well see a 5G in the next 5 years.
Companies: (again, based in the US)
The first company to unveil their 4G network was MetroPCS. Verizon, Sprint, and AT&T now all have phones running on their 4G networks and T-Mobile has one coming next week. Already the big four have outpaced MetroPCS in building out their networks. TracFone has yet to even come out with a 3G network so it is unlikely that they will come out with a 4G network and it seems that they have even stop building out their 2G network so if you are a customer of TracFone, you might be losing your phone coverage within the next few years.