Hey! Well sentence 1 & 2 have the same meaning except that sentence 2 is more specific; outlining where (location) the car is being serviced at. Sentence 1 doesn't provide us with details such as where the car is being serviced.

My car is being serviced - it could be being done at home or a friend could be doing it for you. The second sentence specifies the place - The local garage is servicing my car - not the big garage in the next town, not my friends place but, the the local garage is doing the work.

I feel like the first one is said more often. The only difference between them is that the first one is written in passive voice while the second sentence is written in active voice. There is nothing wrong with writing the sentence either way, but usually for essays that you have to write in school for English, most teachers would want you to write in active voice (meaning that you get rid of the verb "to be" in this case). Active voice is when someone is doing something (the local garage is actually doing something in sentence #2) while in passive voice something is being done to something (in sentence #1 the subject of who is doing the action of "servicing" is not specified). Hopefully that made sense, let me know if it didn't :)

Amy, The meaning is essentially the same. Using the passive of "to serve" instead of the present continuous changes the focus of the sentence from the garage to the car. It allows the "car" to be placed at the beginning, a privileged place in an English sentence.