Learning Question from Recent Out of Town Broadway addict

So, I apologize if this is really basic but I’m going to ask because I know this community is awesome and will have a quick answer. :)

I had barely ever been to Broadway until last year when I saw 15 shows. It’s so beautiful and special and addicting. But the problem is that I live out of town and unfortunately am losing my job in about a week and change.

Anyway, I’ve always bought in advance or lottery tickets to keep in my budget; however, I’ve been excited about Othello since it was announced. I love Shakespeare and the amazing talent involved (not just Gyllenhaal and Washington, so much of the creative team is amazing) got me so excited. I have checked literally every day and it’s just not looking financially responsible under my new circumstances. I am planning to enter the lottery every day and hope I win and drive up from DC if I win; however, I imagine this will be a crazy one to win with lots of competition. So, my backup plan is to go at the end of March and try to find an alternative path to an adorable ticket.

So, my question is inspired by this show but I’m actually just curious in general so I can feed my new Broadway habit when I hopefully get employed again haha. Can someone explain a little bit about the difference between rush and TKTS booth and just showing up at the box office the day of? I’m aware of the Theatr app, I’m specifically asking about TKTS vs rush vs last minute box offuce walk up.

I understand the basics (TKTS is a booth with a bunch of shows, rush is time ensitive in the morning usually, etc), but more specifically…

  1. Are these methods from the same pool of tickets?

2.Do you get any choice in where you sit or is it randomly assigned for cheap like it is for lottery?

  1. With dynamic pricing being such a big thing, do the tickets on the day of get cheaper as curtain approaches? AKA a ticket at the booth or box office might be $100 at 10am but $40 at 6:50pm or something.

  2. Are rush tickets a set price like lottery tickets or are they just a cheaper version of the price based on how good the seat is?

  3. Are TKTS booths usually a better bet for quantity of availability or is it usually random if rush might actually have more?

  4. Anything else that would help me get a better understanding of the differences?

Anyway, I know this is a lot of questions lol so, no need to answer them all. Just grateful for any insights. Thank you!