Are there transit passes or savings cards for Japanese residents?

Does anyone have them and how much do they cost? I don't want to have to use the machines every time we ride the train and I hate carrying cash for the bus while juggling around kids!

Also, are the passes only good for certain trains and do they include buses?

Last year I was able to purchase 21-day passes for our family because we exclusively used public transit while vacationing in Tokyo but the passes could only be sent to countries outside of Japan because they were only for tourist, we also had to carry our passport at all times while using the passes to prove that we were foreigners just visiting. I can't seem to find a website for passes for Japanese residents.

You can get a PASMO card, load some yen on it and bypass the machines and need for cash. It works for trains and buses and vending machines by the trains

I do believe you can get a commuter pass for the trains/busses. I'm not sure how much it is, but I hear it's 30% cheaper than what you would pay if you took the commute everyday to where ever you are going to. I googled it up, out of curiosity and got these numbers. Not sure if they help you or not:

[Tokyo - Yokosuka]
monthly commuter pass : 27,240yen
time required : 1 hour and 20 minutes

The PASMO card seems to be more of what I am looking for for daily travel, but does it lower the price of transit costs?

No, but it makes travel a little easier as you don't have to go to the kiosk every time you travel for every person traveling.

No, PASMOs do not lower the cost. But it's definitely the way to go when you travel by train and bus. Kids under the age of 13 pay half price ...