Would it be possible to pay from the Blockchain app to a Coinbase app in a restaurant? I walk into a restaurant that accepts bitcoins and pull out my phone with a blockchain app to pay with, the waitress then shows me a phone with coinbase app to pay to.. 

Are there any issues with paying from one company's app to another company's app? 

Regards: Beginner bitcoin user
What you really do is to send bitcoins (with a phone app, in this case) to a bitcoin address. So, strictly speaking, Blockchain or Coinbase, if we consider only the send/receive function, are providing you something it's already yours, meaninf that a wallet with its addresses and the send and receive functions are at your disposal for free on the bitcoin network, and you can use them installing one software wallet on the PC.

What is important for them, and is useful for you too, is another function of the app, the one which allows you to buy bitcoins, maybe with no waiting between the payment and the bitcoin "arrival".

All the apps, under the hood, are compliant to the same rules, defined by the protocol. Apps realized by companies like the ones you mentioned must obey those rules: if the don't, are unable to interact with the network, they would be useless. So, all does the same things the same way, as fare as we speak of activities that require to use the bitcoin protol (send and receive the coins)

If you're asking if there is some kind of proprietary/private protocol that makes the use of Coinbase or Blockchain the same as choosing between VISA and American Express: no, as far as I know. It is not possible, because Bitcoin's code is open source, which means everyone can read it and learn how to write its app to send and receive bitcoins. It is not something owned by a company, is something everybody can access for free.

It would be a ruin for Blockchain if you could not send bitcoins away the easiest way possible, wherever you are and to every address in the (bitcoin) world! After all, they earn money because you buy bitcoins from them. The easier and faster you spend your bitcoins, the sooner you'll buy others.

What exists is the opposite. In 2012 was described a way to represent a bitcoin address and to ask to do something with it, all in a line similar to the internet links.

Here you can find the specifications, the document is called BIP21. The simplest example is this:

bitcoin:175tWpb8K1S7NmH4Zx6rewF9WQrcZv245W

An example of use: I send you an email with that URI inside, you click on it on your smartphone, the mail app, that implements BIP21, is aware of the bitcoin URI format, so knows what to do: pops up a requester asking if you want to save the address in the phonebook, for example, under my name, since I am the sender of the email.

Bitcoin took quite a long distance from some of the ways we are all used to relationship ourself with money in general, and with the market, too. Who knows what else will be possibile, given that some big evolutions are not that far.