Greetings,

There are different opinions regarding your question.

1) The Roke'ach in his commentary on the Siddur writes that Geshem is mixed with wind, while Matar falls straight to the ground like an arrow with a target ("Matarah").

2) The Ramban (in his commentary to Iyov, chapter 7) writes that Geshem falls lightly, while Matar falls with force. Some of the Acharonim writes similarly to the Ramban (see Chidushei Rav Shlomo ha'Kohen mi'Vilna (the Cheshek Shlomo, Ta'anis 4b) that Geshem falls coarsely and heavily, while Matar is rain that falls scattered and in fine drops.

3) Some mention that Geshem can be both rains of blessing and of curse, while Matar always refers to rains of blessing. (See Cheshek Shlomo to Ta'anis 2a.)

4) The Aruch ha'Shulchan (Orach Chayim 119) says that Geshem falls from the sky, as opposed to Matar, which is water that has evaporated from the earth and falls again. The Malbim (to Zachariah, chapter 10) writes, on the contrary, that Geshem is natural, as opposed to Matar that falls by special providence from Hash-m. He, too, sees this from the word "Matar" being close to the word "Matarah."

5) Yet others write (see Metzudos Tziyon to Zechariah 10) that there is no difference; Geshem and Matar are synonymous.

There are many Pesukim that are cited to prove each opinion, but the bottom line is that there is no real clear-cut answer.

I hope this helps,

Aharon Steiner