It seems “filter” is more commonly used. So where is “screen” used？
Please screen my file before I present it to these directors.
Please give me a filter to exclude dirty dirt.
An image search will still help you. Look at pictures of "filter", "screen" and "sifter" to see the physical objects.
Think of how these items are used (ie. to filter = to use a filter) , and that will show you the difference between the verbs.
Do an image search for "filter" and "screen". These are both physical objects, and you can understand the difference based on how each one functions.
I'm not sure how "pick up" applies here, unless you mean "detect" (ie. detect something when there are a number of distractions). It'd be far better to post the sentences that you've found.