Short version: UMTS = 3G. LTE = 4G.
Long version:
UMTS was one form of 3G data on GSM networks. GSM was originally TDMA (voice still is) - time division multiple access. In TDMA, each phone takes turns talking to the tower. That's fine for low-bandwidth applications like voice, but was terrible for data because each phone took an equal slice of the tower's time (and bandwidth) even if it didn't need to use it all.
In CDMA, all phones transmit at the same time. The tower uses orthogonal codes to distinguish them - kinda like one person writing on a piece of paper, while another person writes on the same paper at 90 degrees. The letters overwrite each other, but they're distinct (orthogonal) enough that you can distinguish the horizontal letters from the vertical letters. And you can selectively ignore the letters written by one person or the other to read each individual message, even though they both overwrite each other. In CDMA, each phone sees the other phones' transmissions as noise. This reduces the signal-to-noise ratio, and thus bandwidth scales automatically depending on how many phones are actively transmitting or receiving data at any given moment. So CDMA automatically maximizes the amount of bandwidth available to all devices.
CDMA absolutely destroyed GSM when it came to data speeds. GSM conceded and added wideband CDMA to the GSM standard for 3G data, and called it UMTS. The original implementation could hit up to 2 Mbps, though later variants could reach much faster speeds.
4G LTE is the current generation data service. Its original spec maxed out at 100 Mbps, though newer variants can (theoretically) hit 1 Gbps. LTE is mostly based on OFDMA, which is very similar to CDMA but uses orthogonal frequencies instead of orthogonal codes. There are a few LTE channels which use TDMA, except instead of each phone getting a timeslice like in GSM, only the phones which request a timeslice get one, thus allocating bandwidth more efficiently.
Why didn't we jump straight to OFDMA instead of CDMA? OFDMA requires more processing to extricate each orthogonal signal. The processors in early phones used too much power to decode OFDMA to make it usable for a day on a single charge. Early OFDMA standards like WiMax would drain a 2010 phone's battery in about 3-4 hours. Modern processors are much more power efficient and able to last all day while decoding OFDMA.