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I am not sure if this is the right place to ask this question, but I guess that ornithology enthusiasts (or ornithologists) will have the best knowledge about it.
I am wondering if there is a website which would identify birds by their looks. For example, I would specify that the bird is similar to a sparrow in size (just a little bigger), it has a gray back and yellow-ish-orange-ish belly and it would tell me the exact species.
$\begingroup$I've ran into problems today while trying to identify a bird provided as an example in the question on google. Turns out it was a nuthatch - the first website you provided gave me that answer. Thanks!$\endgroup$
$\begingroup$If you're looking at birds in Britain the RSPB's bird identification web pages have worked well for me and it works in a way described in the question.$\endgroup$
If you are on the go, the Merlin app for your smart phone is great. Especially if you are in North America!
Merlin is a smartphone app that you can download via your preferred app provider (apple, google, etc.). It is maintained by the Cornell Lab of Ornithology, and is related to the All About Birds online archive.
The app does exactly what you are looking for, where you specify the approximate size, up to three colors, where the bird was seen (in water, at a feeder, in trees or bushes, etc) and where and when you saw it and it can provide a list of suggested birds. The suggestions have information on identifying the bird species, maps of the species distribution, and example sounds that each species makes.
If you are an avid birder that records your sightings in eBird (also created and maintained by the Cornell Lab of Ornithology) there is an option to add the bird to your "Life List" from within the Merlin app.
$\begingroup$Please add a bit more context to your answer. If your link dies, then we are left with basically no information here. A summary, screengrab, highlights, etc all could be useful. (FYI: don't use the 7 year old other answer as a guide -- our standards have increased since the very early years of the site)$\endgroup$
$\begingroup$There is a proposed edit from "selene" — are you posting using more than one account? If so, you may find this information on merging accounts to be of interest ...$\endgroup$
$\begingroup$So, is the currently pending edit on your answer something you wrote or not? If it is yours, then you are definitely posting using two different accounts (possibly from different devices) and you should merge those accounts. If it isn't, then you should either approve, edit, or reject the pending edit.$\endgroup$