No, your tires don't have to be the exact same pressure. But close is probably good.

We've been getting a lot of new riders in my group, on very old hand-me-down bikes. They have to put a lot of money into making the bike run, and then are still stuck with less-than-modern-day equipment, with all its advantages such as better, easier to work components, more gears, easier to reach shifters, etc. I feel badly that they are struggling with an older bike as well as with riding in general. I feel like a new, or at least only a couple years old, bike would make riding a lot more enjoyable.

Still, it's kind of like having an old paid-off car- easier to get nickel and dimed to death than invest in a new one, if you just can't afford it.