just to give an idea of the most common methods of decoration you're likely to see, here are a few pix which might be of interest.
1.............wheel engraving (same method as your piece) and showing the delicacy which can be achieved. Appears as greyish tones, with lighter areas achieved by less contact with the copper wheel. Outlines appears sharp and well defined. Some depth to the cutting, but very shallow usually.
2.............machine acid etched - infinite variety of designs from geometric to naturaistic images such as this - which looks like it's supposed to be a stag with hind, a tree and bush plus some grass (can't get it all into the pic.). Tends to look shiny but has frosted appearance, and outlines quite sharp. After sandblasting, this has probably least cutting depth.
3.............sand blast effect - lacks quality and seen often on utility tumblers for example. Outlines lack sharpness, and in comparison with other styles mentioned, image has zero depth. Appears as uniform granular texture, and without ability to show tone.
4.............traditional cutting - should be unmistakable. Areas of cutting should be as shiny as uncut parts of the glass, although if looked at carefully some minute traces of scratches often remain within the cutting. Most patterns/designs created initially by use of large abrasive wheels, with varying methods (including acid) used to polish. 'V' cuts, or mitre cuts (as shown enlarged in pic 4) are very common - are sometimes very deep - but will always be deeper than any of the preceeding methods.