Why are the same alloys solid in solder wire and liquid in solder paste?

Solder paste is actually composed of tiny solid balls of solder suspended in flux, so it's not a liquid it just seems like it without a magnifying glass or microscope. The wiki article goes into more detail about the different sizes of solder balls if you're interested in reading further

The solder granules in solder paste are actually solid, and can be of the same alloy as wire solder.

The flux itself is what is liquid, to facilitate its application onto the circuit board and hold the SMD components in place as hot air is applied to solder them to the board.

• Soldering paste is meant for soldering SMD parts on a circuit board. Only hot air (or another heat source that doesn't touch the paste) is required.

• Wire solder is meant for hand soldering other, larger jobs using a soldering iron.