Stammer and stutter are the same thing. In the UK we typically say stammering, in the US it’s stuttering. It’s possible that you’ve always had a stutter but it’s gone under your own radar and is now somewhat more prevalent due to the stress you’re under. An acquired stutter (as opposed to developmental) is also a thing - but this is more likely to occur through significant trauma (like a head injury). It’s also important to note that every verbal human on earth stutters at some point, but for some people, like me, it’s a constant part of their speech. I think from the sounds of things you’re stressed and it’s encompassing you. That’s normal, but I think you should try and relieve the stress to see if it has any impact on your speech.