There are some words with un-pronounce letter in Russian. Usually they appears if there is too much consonants together.
For example, we write "солнце" (sun), but it sounds like [СОН-цэ], without the "Л" (notice: 3 consonants together — л-н-ц). Even native speakers can't explain why (may be, only linguists can). But "Л" is pronounced in similar words, though: "солнечный" [СОЛ-нич-ный] — "sunny".
I suppose that "пожалуйста" takes origin from the word "пожалуй" (it has complicated meaning, from very polite and affable form of "come" to "perhaps, very likely" and even "pay salary"). "Пожалуй" sounds like [па-ЖА-луй] and you really hear the "Й". But when "ста" was added to "пожалуй", "й" became un-pronounced (and again: й-с-т, three consonants). So usually we pronounce it like [па-ЖА-лу-ста] or even [па-ЖА-ла-ста].
Note: the un-pronounced consonant is not a rule, it's some kind of exception. Usually 90-99% words with 3 and more consonants are pronounced with every consonant: естество (nature) — [ес-ТЕСТ-во], you can hear all the с-т-в "chain".
Thank you for your explanation. About your final note though, I think this has to do with syllable boundaries. You did cut the syllable between [ст] and [во], aftee all.
The same can be observed in English. Compare “knowledge” to “acknowledge”: the letter 'k' is silent in the first word while it is heard in the second word.
Just my two cents, really. I know next to nothing in Russian but took linguistics at uni.
There is no difference, just different ways to spell it (borscht, borsch, bortsch, borshtch, borsh, ...)