marriage = the ceremony of becoming husband and wife considered from a purely religious or legal point of view
Her parents are against the marriage

wedding = the occasion when this ceremony takes place and the celebrations that follow it
I never see most of my relatives apart from at weddings.

• Why didn’t you invite me to your marriage? ✕
• Why didn’t you invite me to your wedding? ✓

• I have just received your marriage invitation ✕
• I have just received your wedding invitation ✓