some thoughts on these glasses, in reverse order.
I would agree the second piece is from somewhere in the last third of the C19. This shape/design was very popular in the second half of the C19 - seen often with coloured bowls in green, red and more rarely blue which were for white wine or pale sherry apparently, whilst the completely clear examples like yours were for sherry only. It seems that pieces with a collar/merese under the bowl are possibly a little earlier than those without this feature. However I suspect that like so many things production might have been for longer than we imagine.
Poorly shaped cyst and very irregular foot indicate a pub/tavern glass, possibly. I can't see the pic clearly to know if there is a ground/polish pontil depression - there would be, usually.
As for the first glass, it looks an unusual design. I'd suggest in view of the length of the stem a goblet rather than a rummer (rummers have stems that, usually, are disproportionate to the size of the bowl).
Is it lead glass - again I can't see clearly if it has a ground/polished depression under the foot - what is the colour of the glass - is there the sort of wear you'd expect from a glass that comes from somewhere between about 1880 and 1915 (art nouveau period).
I could be very wrong, but that rather smooth shiny underside to the foot, plus what appears to be a very narrow rim under the edge of the foot, might suggest this is a modern glass.