What is the difference between Unique Key and Index with IsUnique=Yes?

Creating a UNIQUE constraint is a clearer statement of the rule. The IsUnique attribute of the index is an implementation detail - how the rule is implemented, not what the rule is. The effect is the same though.

There is a clear difference between the 2. A unique constraint defines what combination of columns has to be unique. A unique index is just a way of making sure the above is always valid. But it's possible to have a non-unique index supporting a unique constraint. (if the constraint is deferable = Only has to be valid at commit time but is allowed to be broken in the middle of a transaction)

Just so that you know, when you create a unique constraint SQL Server will create an index behind the scenes

One thing I just found out the hard way is that in SSMS scripting of unique keys was set to true by default but the scripting of indices was set to False. When I used the Script Table As context menu from SSMS I didn't get my unique indices.

Also if the type is set to Unique Key, you can't change the "Ignore Duplicate Key" setting. First you have change the type from Unique Key to Index then you can set Ignore Duplicate Keys to true.