杯
bēi
You're counting the cup, not the drink: 杯
The picture One cup held in your hand. Whatever fills it, what you count is the cup. 杯 is as much as one cup held in your hand; 瓶 is as much as one capped bottle you carry around.
Where the picture shows up in 杯
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one at the café
我要一杯美式咖啡。
wǒ yào yì bēi měishì kāfēi
One americano, please.
Setting an empty cup on the counter and filling it with coffee.
In a bottle it's 瓶; in a bowl it's 碗. Change the vessel and you change the counter.
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one you ask for
请给我一杯热水。
qǐng gěi wǒ yì bēi rè shuǐ
Could I have a cup of hot water?
Holding out an empty cup in both hands to ask for hot water.
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two more you order
我们再来两杯啤酒。
wǒmen zài lái liǎng bēi píjiǔ
Two more beers, please.
Raising two drained glasses to order another round.
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the one you adjust
这杯奶茶少放点糖。
zhè bēi nǎichá shǎo fàng diǎn táng
Less sugar in this milk tea, please.
Pointing at the cup in your hand while asking for less sugar.
All of it in one picture
What gets filled at the cafe is one cup, what you ask for is one cup, what you order again is two glasses, and the milk tea you adjust is one cup. 杯 does not ask whether the inside is coffee, water or beer; it asks only whether it fills one cup. So anything counted with 杯 brings a size with it: as much as one cup in your hand. Pour the same drink into a bottle and it becomes 瓶; into a bowl and it becomes 碗.