There are umpteen different implementation of Maestro in Europe, the UK and Rep. of Ireland are just two of many. None, or at least very few, can be accepted over the internet outside their country of issue at present.
The Maestro facility is basically an add-on that allows the cards to be physically processed by a card terminal in a shop, or at an ATM when abroad.
I'm guessing that Maestro will get standardised at some point in the future as a debit card sollution that works across the EU properly.
Right now, most Laser cards in Ireland carry Maestro co-branding. When used online or over the phone, they're still Laser cards. Only when they're used physically in a chip and PIN machine outside Ireland does Maestro come into play.
Laser and Maestro actually sit as two seperate applications on the chip, the card reader will even sometimes ask Laser? Maestro?... and the card can process using either.
The UK Maestro debit cards are basically just rebranded Switch (the UK's equivilant of Laser). MasterCard international took over the UK's Switch brand and relabled it Maestro, but from a technical point of view their cards are still just Switch with a Maestro co-brand.
Maestro's also used in Germany, France, Spain etc etc. It's quite commonly issued but almost always as an add on service.
What's causing confusion is that the UK's switch cards were fully rebranded as Maestro, but remain technically restricted to being Switch cards i.e. they can only be accepted online / on the phone in the UK, and UK online merchants accepting Maestro can only accept UK maestro as it's really switch!
(Confusing or what?!)
UK Maestro cards can't be accepted online by say German Maestro retailers, nor French ones etc.
But, they can be accepted physically in a chip and pin terminal
Same goes for Laser.
Basically, the only debit cards that work fully internationally online are Visa Debit (Issued only by Halifax in Ireland at present)
MasterCard debit also exists, but no Irish banks issue it.
Visa Electron is also widely accepted, but again none of the Irish banks use it.
Basically, our banks seem to be wedded to Laser which is quite restricted in terms of what it can do.
I'd say though, given that Halifax launched Visa Debit, someone else will too before long. There's nothing stopping them from doing it as it uses the Visa credit card infrastructure.