What is the difference between present-day and modern-day?

They are often used interchangeably, but there is a different connotation. Present-day compares current things with those in older times mostly to show differences. Modern-day dwells on the progress or development of things over time.

Examples: Present-day cities are much more crowded than in the past. Modern-day medicine has found vaccines to cure many serious diseases.

modern day refers to a period of time(which is the most recent). present day refers to now, today,tomorrow! right this moment!

Present day means now and every new day is the present day. Modern day means the age we live in and is as old as the oldest perspon, so last 100 years or so would qualify.

Present-day can mean this year, and modern-day can mean this century.