First you have to know the difference between on and kun readings. On refers to readings that come from Chinese. Kun refers to readings that come from Japanese. Most of the time it is pretty easy to tell which one comes from Chinese and which one comes from Japanese, due to the stark differences in pronunciation. Kanji websites will tell you which is which when you search one up. After a while you'll start to spot the differences.
There is a phenomenon in English where words from French and Latin occupy a more formal register compared to their native English counterparts. An example is native English 'father' vs Latin 'paternal'. You can see that both words arguably have the same meaning, the only difference being the 'formality' of the word. This phenomenon is also present in Japanese, with words borrowed from Chinese being more formal. Examples include Japanese hito vs Chinese jinrui, Japanese onnanoko vs Chinese joshi.
Now if we apply the above to your two words, we can see that jidousha, with its on readings, is used more formally than kuruma, which is used less formally. Otherwise, they have the exact same meaning. You can use either one you want depending on whether you feel it.
Basically what Hatareizu said,
"自動車" is something like "motor vehicle", whereas "車" would be the simple word "car".
ありがとうございます!
Cool explanation brah
When do you use 自動車 and 車?
I've heard 車 being used more often than the other.