The voltage difference is the easy to solve, just get a voltage convertor from Best Denki or Harvey Norman for $10-$15.
It is the "band" that is a headache.
In the U.S., analog cellular phones operate on a 800MHz frequency band, and their digital PCS phones support a 1900MHz frequency band. A dual-band phone to them means it can utilize both the frequencies. Analog is still being used in alot of the areas outside the major cities.
"Mode" simply refers to whether or not the phone supports analog or digital technology. A dual-mode phone supports both. This way, if you're in an area that doesn't support digital you can still make an analog call. Tri-mode means that the phone can support two different digital transmission technologies as well as analog. It can also mean that the phone supports the same digital transmission type at two different frequency bands, such as CDMA 800 and 1900.
In Europe, all of them are on GSM just like Singapore and HongKong. In China, they are on both GSM and CDMA/WCDMA.
I assume you are refering to US, since they are the biggest users in terms of absolute numbers of users. The most common transmission technologies for US mobile phones are as follows:
AMPS Advanced Mobile Phone System. Analog transmission technology that operates in the 800MHz frequency band.
TDMA Time Division Multiple Access. Digital transmission technology that operates in either 800MHz or 1900MHz frequency bands. The frequency band is split into a number of channels, so that several calls or data can share a single channel without interfering with one another.
CDMA Code Division Multiple Access. Digital transmission technology that operates in the 800MHz or 1900MHz frequency bands. CDMA spreads the information contained in a particular signal over a much greater bandwidth than the original signal.
GSM Global System for Mobile communications. Digital transmission technology that operates in the 900MHz and 1800MHz frequency bands in Asia and Europe, and 1900MHz in the U.S. GSM is currently the dominant digital mobile phone standard for Europe and Asia. While not originally popular in the U.S., many carriers are beginning to switch to GSM technology.
Now, if you are a traveller in the US, then you will need AMPS, CDMA, & GSM to cover all grounds. If you are in Singapore and travels to US occasionally, use the local TRI-BAND; GSM 900/1800/1900 should suffice. If you are buying from the US, just make sure they have GSM 900 or GSM 1800.
However, I should point out that all the phones you get there are simply not as nice or small as the ones you get here in Singapore and HongKong. Another thing, 6 months....Singapore and HongKong get all the newer models of phones here almost 6 months ahead of US. Example, when I first got my Motorala V60 here in Singapore thru DBS Bank, I went to US 4 months later, the Motorola sales people were surprised literally that I am already using it. They finally got it forsale 2 months later, an twice the price they sell here, for plans costing 3 times more per month.