Making the jump from a Boehm-system flute to a folk or traditional flute can be rather simple, but there can also be bumps in the road. One of those bumps might be the slight differences in how to play certain notes.
One of the most important things to remember is that when you’re playing your Boehm-system flute, there are all sorts of buttons and levers rods and gizmos (my favorite!) that help do a lot of the work for you. On a simple system flute, those are not usually there.
On a Boehm flute, we use a 1-2-3-1 fingering to play the note F-natural. However, on a simple system flute, that same fingering will produce an F-sharp. Why? Think about the mechanics of the Boehm-system flute. When you put down that right hand index finger, the mechanism of the flute closes two holes for you. When you switch and use the right hand third finger instead, the mechanism of the flute does something different, and only closes one of the holes. That hole is the difference between F-natural and F-sharp. The mechanisms of the flute gave you the option to do one or the other. But remember that this option was added to flutes after simple system flutes already existed. So really, one way to think about it is that your Boehm flute has been helping you cheat all along!
If we think of the Irish flute or whistle as a diatonic instrument, giving us a D major scale, almost everthing lines up, with the exception of the F-natural fingering (if you’re thinking Boehm) to produce an F-sharp, as I described above. However, as I also noted in Instrument Key Naming, we’ll often use a whistle in D to play a tune in G major. How does THAT work, with D major containing C-sharps, you ask? Well, you just play C-natural!
If you try to play the same fingering for C-natural that you use on a Boehm-system flute, you’ll quickly be disappointed, because you likely don’t have a left-hand thumb hole to open, as you do on your Boehm flute. So by trying to play a C, you just end up playing a B. To play a C-natural on an Irish flute or whistle, you’ll leave up the first finger (which would normally produce a C-sharp), but then lower the 2nd and 3rd fingers on the left hand to bring the pitch down a half step to C-natural.
Beyond that, you’ll find a number of “trick” fingerings for certain notes, but they are quite often dependent on the type of instrument you’re playing, or maybe even the particular instrument maker. When you buy the instrument, you can often ask for a fingering chart that will help you with trick fingerings, but discovering them on your own will help you become more accustomed with your instrument and really internalize the various options you have for each note.
Those options could include cross fingering (sometimes called fork fingering), where, just like with finger Vibrato, you would skip an open hole from the last hole you covered, and then cover that finger hole, and occasionally the next one as well. This helps to lower the pitch of the primary note by (sometimes) up to a half step.
Another option could be half-holing, in which you literally cover half a finger hole to (hopefully) find the pitch halfway between the two notes that are diatonically available to you.
Both of these methods are worth experimenting with from time to time. You might find that each has their own place, depending on the particular note or even just in one phrase of a particular tune. Again, experimenting and trying out things you think might not work can sometimes give you the best results!