Okay, sure a screaming toddler can be irritating, to us.
They have all sorts of reasons for screaming.... so pinpoint what the reason is.
They are either: tired, frustrated, hungry, because they cannot yet do what they have imagined in their heads, because their coordination/motor skills are not like how they want yet, because their emotions are NOT yet developed, because they are also getting new 'abstract' emotions which they do not yet understand, they are becoming more independent and flexing their sense of self etc.
For me and my screaming kids (LOL), well I react/trouble shoot it per the situation. Not all 'screaming' means they get scolded. I don't do time-outs to my kids myself, but I do time-outs with their toys. Time-outs on my kids, do NOT work.
Sometimes too, a child is just experimenting with their own voices... they do not yet know or understand subtle voice inflections/innuendos and what they mean. And sometimes they just think it's funny.
My kids both have trumpet voices, whether or not they are happy or angry. But, I will 'whisper' to them, to calm them down... or when they are angry... or just yelling for no reason... and often, this will work and I tell them to copy Mommy and whisper too. Then, it changes their 'mood' and triggers another more palatable behavior in them.
BUT, also at this age, you can begin to teach them about 'feelings' and expressions and how to constructively react to it. (ie: "Even adults get angry... but we TRY not to take it out on others. If you need to yell, you can go in your room.... or hit a pillow. OR, you tell Mommy you are angry and I will help you...") I taught my kids about emotions and the names of it and the expressions for it, at this age. And they then could tell me how they feel... thus, deflating bad moods. But it takes time, and repetition.
Just telling a kid "no" does not always work.... they just tune you out. So, try a toy time out.
BUT, sometimes a kid just has to get their yah-yah's out... and screaming is a way they do it. Getting out their pent up whatever. Or, make a game of it, or play Simon Says... that is what I do. Or, encourage them to SING...instead. Thus, teaching them DIFFERENT ways to use their naturally loud voices.
My kids have such naturally loud voices... I can't make them have muted voices. It's just the voices they were born with. So I just try and redirect it... or, if they are being "naughty" I do the toy time-out. And, I kneel down to their height, whisper, and direct them to what I want them to do. Then they deflate.
Growing pains. It will pass believe it or not. My kids are 2.5 years old and 6 years old... I go through this too.
BUT, I do not 'punish' for 'happy' voices even though it is loud. Its a tolerance thing, and my wanting my kids to grow up with robust ability for expressing themselves. And they DO know when and where certain voices are appropriate or not. For instance, when in a store or at home.
*adding this: at certain times of the day, I just KNOW that my kids get more 'yell-y". They are getting out their yah-yah's. So I let them. After that, I KNOW they will calm down and not yell. Also, at certain times of the day, it is "quiet time." My kids know this. It is a DAILY 'routine', so it is enforceable, with just my telling them "quiet time." It takes practice and repetition.
All the best,
Susan