When it comes to card business, almost everything is different between US and Europe. US market is huge and very mature. US never migrated to EMV, while Europe has almost completed the migration. (Well mostly)
EMV is the defining point between these two markets. Europe has chosen the card to be the safest and made a huge investment. Now European cards have the ability to process an offline PIN, validate itself to the POS terminal prior to online authorization, generate dynamic signature of each transaction (cryptogram), validate the host system, etc. In the US, POS terminals just read out the mag stripe data and send the transaction to the issuing host for authorization.
In this context, contactless transactions work in the same way. US contactless cards just send the mag stripe data over RF interface instead of the mag stripe reader and everything else is almost the same. However, there’s a slightly different security enhancement which may change the things. Each contactless transaction is sent to host by generating an unique transaction counter, which can not be done in the mag stripe world. Big step.
In Europe, contactless transactions are offline. Visa and MasterCard release specifications for online too, but this was just for compliance with the US network. Offline means the card application needs to authorize the transaction without asking to any central host. To be able to do this, you just need to have a smart application inside the chip which can store some smart decision making data. This is the main difference between Europe and the US.
In the US, contactless only chips can be used without any interaction with the mag stripe. But in Europe, this is simply not possible. The chip needs to be dual interface, meaning that it should work both from contact and the contactless interface.
With the introduction of contactless payments, US market began developing into another era, while for Europe, it was a natural extension to the contact applications. Once again Europe choses the expensive and the safest way while US goes from the opportunistic path.