How can I tell the differences between a 3G, 3G LTE, and 4G phone? I apologize if this is the wrong place to ask, but it looks like the Gadget StackExchange has been closed.

I've been doing research on mobile phones and looking at different Android devices and I'm a bit confused. Often times, the device advertises 'Speeds up to X Mbps', and lists the available networks (e.g. GSM, HSPA/WCDMA). However, as 3G LTE and 4G standards have been developing, phones are being released that are capable of even greater speeds.

How can I tell if a mobile is 3G LTE or 4G? Can a 3G LTE phone upgrade to 4G? (And for that matter, is there any difference between WiMAX and 4G at this point?)

Thanks!
First, WiMax and 4G are completely separate.  WiMax already has real-world implementation, whereas 4G does not; 4G is still in development.

Second, 3G LTE is also completely separate from 4G.  LTE also has real-world implementation.

A 3G LTE phone can only operate at 4G speeds if it has hardware capable of it.  The manufacturer will undoubtedly advertise this, so it shouldn't be hard to find out.  I know of no current phones that can do true 4G, which makes sense given that 4G doesn't really exist yet.  The same applies for "regular" 3G phones working at LTE speeds.  The Samsung Vibrant, for example, works on T-Mobile's "fake 4G" network with slightly improved speeds, but does not take full advantage of it.  The Vibrant 4G, however, does take full advantage of the higher speeds.

Currently, cell providers in the US and elsewhere are referring to various 3G technologies including LTE, HSPA+, etc. as "4G" when they are not actually 4G.  Examples of 4G networks in development are  LTE Advanced (based on 3G LTE) and WirelessMAN-Advanced (based on WiMax).

Speed requirements for 4G service set the peak download speed at 100 Mbit/s for high mobility communication (such as from trains and cars) and 1 Gbit/s for low mobility communication (such as pedestrians and stationary users).  3G LTE and WiMax do not meet these speed requirements.

The Wikipedia page on 4G is quite informative.