For my sister's wedding I had party make up done on her mayoun and shaadi day. It was basically heavier make up than every day wear, but not as heavy as bridal make up (less eye shadow, no fake eye lashes, less foundation).
I think party make up is more if ur having ur hair and make up done for some1 elses wedding. Like i had my hair and make up done when 1 of my close friends got married-that was party make up-not so heavy on the eyes and the base wasnt as full on as it is with bridal make up. Plus the hairstyles r different for party whereas its way more elaborate for bridal.
Sara, if you're going to a desi salon in the US, definitely go for a trial. You're right about the difference between party makeup and bridal makeup, but the salons here already have a fairly light hand when it comes to application. For a wedding, you're probably better off with bridal makeup.
At salons in Pakistan, a lot of brides go for party makeup (or even "engagement" makeup) because it costs less and it's looks better in real life. It's still very polished without being caked on. You know how heavy the bridal makeup is in Pakistan.