- is that it seems using EMV method cant give the user any benefit of any available multi-use price discount that the transit company may offer, whereas the transit card can use multiple trip discounts that the transit company might offer.
They can in an EMV open loop system. How it works is that every time you tap the card number is recorded. The taps are sent to a central server at the end of the day where the travel path is computed and the appropriate discount and passes applied. The whole day's charge is then sent to the bank for billing.
Many systems do this like London and Chicago. For example, London has a daily and weekly maximum cap on fares, so your use is stored for a week. Chicago lets you buy a pass and link it with your card, so you won't be charged.
how about with a dedicated transit type of card: are these cards basically stored value cards that need to be recharged?
Correct, this is identical to Suica, PASMO, etc. though it is common to have auto recharge via a link with a credit or debit card. The major difference is that in many places in the West, you or your employer get tax benefits paying for transit, so they can't permit these cards to be used for vending machines, McDonalds, etc.
The transit agency has to maintain accounting, payment handling, compliance with financial laws, production and distribution of cards, etc. which ends up usually costing them more in total than the EMV system. This is why many transit agencies worldwide in places where people have high usage of credit and debit cards are going to EMV/contactless.
there seems to be two different systems, depending on the city, correct?
Most cities are stored-value only or have both contactless and stored-value, like London. Chicago was one of the few cities (perhaps only) to go contactless only; if you didn't have a contactless card, they sold you a prepaid debit card with the Mastercard logo that you could actually use elsewhere.