This is a mood difference, not just a verb tense difference.
of or relating to the verb form that is used to express suggestions, wishes, uncertainty, possibility, etc.
Your first sentence expresses a wish, a wish that someone does not go to work. This expression is achieved by switching the tense to the past.
The second sentence is more of a command because it remains in the present tense.
I would rather we ate turkey for Thanksgiving.
I would rather we eat turkey for Thanksgiving.
The first sentence is quite vulnerable, it's a suggestion, it's an opinion, it's a wish. While the second sentence is more asserting, demanding, obligatory.
If I had wings
If frogs ate zebras
If ants were people
These are all phrases that express a probability, possibility and doubt, and are therefore considered subjunctive phrases.
On the other hand,
If I have wings
If frogs eat zebras
If ants are people
All of these phrases are in the present tense so the doubt is gone.
If frogs eat zebras, they become giraffes.
Even though the above sentence doesn't describe something that is naturally possible, it is in the present tense, and it assumes the reader knows that frogs are capable of eating zebras.