250 ml is a metric cup and we call it “a cup”.
5 ml is a metric teaspoon and we call it “a teaspoon”.
15ml is a metric tablespoon and we call it “a tablespoon”.
Thankfully, my kitchen scales and measuring jug are both bilingual so I can weigh ounces and pour fl. oz if that’s needed. But in recipes with cups and teaspoons, I just use the metric. Ditto for sticks of butter (I use 125g for that, what’s 7g going to hurt)
Sadly, many American baking cookbooks do indeed ask you to bake by volume. Oh, they try to get around the subject by going through a big song-and-dance about how to get a proper cup of this and that, but I’m sure it leaves many beginning bakers confused and annoyed.
(And it doesn’t even have to be $30. I think I got my latest scale, accurate to an eighth-ounce or gram, for $15 via Amazon, and it was highly rated by various sources.)
I’ve baked from scratch for two decades and change, and spent a year baking for my job. The number of times I’ve used a scale while baking has been minimal. It’s really not that hard to bake by volume.
I do not “bake” often, but I cook every day. In general I do not measure ingredients with tools. A friend couldn’t comprehend how I could come close to being accurate, so we did an experiment. Using some old oregano and paper plates, I used my palm to measure out 1/4, 1/2, 1 tsp, 1 Tb. All were accurate. I poured 1/2 cup of water, then measured and was very close.
Some of your smarter digital scales will translate between ounces, grams, and litres with the press of a button. I’ve one that does this. I’ve not checked it’s acccuracy but it seems to work.
The accuracy of the conversion will be perfect to within the accuracy of the scale. (As long as the fluid you’re measuring has a density close to that of water.) The scale just changes what factor it multiplies the voltage from the pressure sensor by.
The standard recipe book that I grew up in in the Netherlands lists how much 100 ml of a number of standard ingredients weigh, and I’ve often used that to measure out ingredients. A lot of measuring vessels will indicate not only the number of milliliters, but also corresponding weights for some key ingredients. Teaspoons and tablespoons are commonly used as well, but I’ve never seen recipes refer to cups of anything.