I'm trying to replace my light switch with a new one. The switch has two switches on it. The replacement switch I bought has two switches but is slightly different than the old one. This as far as I can work out is because the bottom switch is a two way switch. Will I be able to use this new switch?
Yes; just wire it up as it is now. The terminals should be labeled the same.
Note that US/Canada and the rest of the world have different definitions for 2/3 way - in Aus, 'two way' means a light that is controlled by two switches, while in the US, that would be called 'three way', because each switch has three connections.