Difference in meaning of sentences

[Tan Elaine]

I would rather have stayed at home.

I would rather stay at home.

Is the first sentence in relation to the past, while the second relates to the present?

Thanks.

[5jj]

I would rather have stayed at home.

I would rather stay at home.

Is the first sentence in relation to the past, while the second relates to the present?

That is correct in theory:

We went to visit my in-laws last week; I would rather have stayed at home.
We are going to visit my in-laws to morrow; - I would rather stay at home.

However, you will hear:

We are going to visit my in-laws to morrow; I would rather have stayed at home.

I recommend that you do not do this.