Hi - May we see pix of the underside of both please. These pieces may well be from the same source, but in the absence of conclusive evidence you may have to settle for 'possibly'. Most Irish glass is unmarked, and it's from other features that we have to make decisions.
Looking at the lozenge shaped stopper with its very simple wheel engraving, plus the ornate 'feather garland and scattered stars' - then either the Cork Glass Co. or Edwards of Belfast were makers of similar pieces, but that's not really an assertion of proof, just my suggestions as to possibilities, and I'm sure others here will have their own thoughts. The shape is possibly a taper - c. 1800 - 1820 - maybe.
As to the rummer - yes, it's very typical of Irish examples from c. 1820 - barrel shaped bowl, thick strong probably cushion knop - thick and heavy looking foot, and the sort of wheel engraved decoration you'd expect for Irish.
Nice pieces - how were they sold to you? presumably without a suggested factory name. There's a lot of Anglo-Irish glass out there and identifying a maker is very difficult in the absence of proof. Suggest you get a copy of Phelps Warren's book on Irish Glass - the later edition if possible - and Andy McConnell's 'The Decanter Book' will also help. As for rummers, then Timothy Mills book 'Rummers - A Social History Told in Glass' is indispensable. Most of the information I've used here comes from these sources.
P.S. It's common practice here to provide dimension of glass items - can be a help in some circumstances
