I encourage "My girlfried" to consider this, from the link provided by my colleague, and if she should have issues with ÚJČ's position, to take it up with them:
Tvary minulého času se u nezvratných sloves tvoří příčestím plnovýznamového slovesa a tvary slovesa být. Ve 2. os. j. č. lze příslušný tvar slovesa být (jsi) nahradit pouhým -s připojovaným k prvnímu přízvučnému slovu ve větě, nejčastěji jím bývá právě příčestí: Udělal jsi / Udělals, co jsem ti řekl? Byla jsi / Bylas včera doma? Ty jsi / Tys tomu dal! Viděl jsem, že jsi / žes přišel. Podívej, co jsi / cos natropil. Podoby se jsi se považují za základní, neutrální způsob vyjádření. Podoby se -s jsou hodnoceny jako hovorové.
Many native speakers are entirely befuddled by the distinctions between "nespisovná" and "hovorová" čeština. All I can say is that our team should not be blamed for that state of affairs.
I would say that glad is now more rarely used in UK English than happy - it's slightly old-fashioned. In colloquial use, you're far more likely to hear happy. I agree they do have slightly different meanings but any distinction is slipping out of view in general usage, so they are definitely interchangeable in UK English.
I would have said they are slightly different, with "happy" being perhaps a bit stronger than "glad." At the same time, I'd also say they're used more or less interchangeably, at least in the US, in the general "I am XXX" context.
Here is what the Oxford English Dictionary has to say. Looks like the basic meanings are about the same, but one rather than the other may be used, depending on the context.
It probably comes down to the difference between the meanings of the words on the Czech side,...
This determination requires much more than a quick dictionary lookup because the core meanings in both languages can be blocked or enabled by the rest of the sentence.
If the bare "happy" is used predicatively (s.o. is happy, period) or attributively (a happy person or even "glad tidings"), it will mean "šťastný". The predicative "happy" will become "rád" when it comes with a dependent that- or infinitive clause (happy/glad that you are with me, happy/glad to be here), but it can also become "spokojený" when followed by "with the outcome" (spokojený s výsledkem).
All I can recommend to a serious student is to peruse ngrams for English and, while ngrams does not offer Czech, google books for Czech, to map out the partial overlaps of the acceptability of happy/glad/content and šťastný/rád/veselý/spokojený depending on the individual applicable grammar structures in the two languages.