For context, the verses are:

וַיְגָ֖רֶשׁ אֶת־הָֽאָדָ֑ם וַיַּשְׁכֵּן֩ מִקֶּ֨דֶם לְגַן־עֵ֜דֶן אֶת־הַכְּרֻבִ֗ים וְאֵ֨ת לַ֤הַט הַחֶ֙רֶב֙ הַמִּתְהַפֶּ֔כֶת לִשְׁמֹ֕ר אֶת־דֶּ֖רֶךְ עֵ֥ץ הַֽחַיִּֽים׃

And he garash-ed the man, and put to the east of Eden the Cherubim and the flaming turning sword, to guard the path to the tree of life

and

וְאִם לֹא תוֹרִישׁוּ אֶת יֹשְׁבֵי הָאָרֶץ מִפְּנֵיכֶם וְהָיָה אֲשֶׁר תּוֹתִירוּ מֵהֶם לְשִׂכִּים בְּעֵינֵיכֶם וְלִצְנִינִם בְּצִדֵּיכֶם וְצָרֲרוּ אֶתְכֶם עַל הָאָרֶץ אֲשֶׁר אַתֶּם יֹשְׁבִים בָּהּ.

But if you do not yarash the residents of the land before you, they will be stings in your eyes and thorns in your side, and they will harass you on the land in which you are residing. (last half adapted from nJPS)

So in these two contexts alone, the words look somewhat similar in meaning. However, in other contexts they are more distinct.

g-r-sh is mostly about expelling, driving out. It's used as the verb for divorcing. It's used in Genesis 21 as what Sarah wants Abraham to do for Hagar. It is also used for the other inhabitants of the promised land occasionally.

y-r-sh, on the other hand, is about coming into possession of something. It is used to mean "inheritance" in the land--the word for inheritance is yerushah (and in cognate languages it generally means "to inherit"). See Deuteronomy 2:5 for an example of this. It can mean to dispossess, i.e. to come into possession of something by dispossessing someone else. It's used most frequently in the context of the promised land.

So while they're similar, the sense is somewhat different. Garash is about kicking out, expelling. Yarash is about dispossessing, or inheriting their stuff by force. Note that the 1980 JPS translates it as "dispossess".

You're not the first to note the similarity, or at least think they're similar. The Targum uses tarakh for both these words, meaning "to chase out".

Sources: Brown-Driver-Briggs lexicon