advice needed- possible deferment?

I am having difficulty paying student loans due to sudden financial changes. In the middle of a move and my partner lost their job after I had already put my notice in at mine and we’ve already committed to moving across the state. I have a month left at my job, and then will be without income until one of us manages to find a job in the new town.

I’ve been looking into some of the options for dealing with my student loans in the meantime, but I am a recent grad (first gen) and very overwhelmed.

I’m a bit confused on the difference between applying for the unemployment based deferment vs the temporary financial hardship one, and how long the process will take. my auto pay is set for next week and I can pay it if I absolutely need to but it would put a lot more stress on my finances. This all happened extremely fast so I am just not sure what the best option is.

any advice appreciated! tia 🙏