The difference is that the former is not caring about what is said and the latter is intentionally not listening.

To turn a deaf ear means: to put it aside. No matter what is said, it seems to be inaudible. It describes a lack of attention or concern.

And turn a deaf ear: describes intentionally not listening to others.

Expanded Information：

置若罔闻出处：明-朱国祯《涌幢小品》："沈宜厉声力折，只因心中恼他，置若罔闻。 It refers to the criticism, advice, request, protest, etc. to ignore.

From: ? The Book of Songs - Name of a Name - Banner Qiu (旄丘).

Reference:

Baidu Encyclopedia - Turn a deaf ear