First,  when you search " Exotic Car Rental Miami " , the link up above us, which has no exotic car rental miami in its title,  Displays their full title of " Luxury Car Rental Miami Florida "

Second, when i search " Luxury Car Rental Miami " on google, it still doesn't show my full title. it still only shows the first half

the reason i added Exotic Car Rental Miami and Luxury Car Rental Miami to my title, is so i can rank high for both. but then when i look at the search results, (regular and incognito) it shows only the first half of the title.

I looked at the cached version of my website , clicking the the green arrow as you said, i saw the full title on page source. Confirming to me that the whole title got crawled.

if, as you said, google shows the most relevant part of your title, if i search luxury car rental miami, shouldnt it show my full title ?

It just confuses me that other websites show their full title  when i search exotic car rental miami and luxury car rental miami

i see what you're saying

For my website, " Prestige Luxury Rentals ", i have the tile " Exotic Car Rental Miami - Luxury Car Rental Miami (57 characters)". when i search my websites name or the entire title on google, my full title shows up. Fine but, when i search the keyword " Exotic Car Rental Miami ", it only shows " Exotic Car Rental Miami " on my website's title. The meta description fully shows but not the title. What's the issue here?

Also, i dont understand what you mean by

"" If I click to see the cached version (it was cached on May 12) and look at the source, I see the same thing, with a slightly longer title, Exotic Car Rental Miami - Luxury Car Rental Miami Florida.

It wouldn't be odd for Google to shorten the title in the case of my search on the URL. (When I search for the full title, I see the full title in the SERP.)

Did you do an anonymous search when you were checking? You might be picking something up from your own history """ ??. I'm new and still learning

I basically changed the title and meta description of my homepage and when i search on google, it still shows old. Whats the issue?