To seem is always to resemble or to appear.
To look primarily refers to sight, images coming through yor eyes - you can tell people where to look, "look at this!"; you can tell people what you are looking at or where you are looking. It can also be used for searching - "I am looking for my lost dog."
LOOK LIKE = SEEM
To look takes on the same meaning as to seem when 'look' is used with 'like'.
"You look like Charlie Chaplin." (= You resemble Charlie Chaplin.)
"It looks like it's going to rain." (It appears (that) it is going to rain.)
Or, if it's a purely visual appearance, you can leave off the 'like':
"You look terrible." (Your visual appearance is terrible.)
You can use "look" only when something is recognised visually. Some people might argue that that's true, strictly speaking, but in practice "looks" is sometimes used more widely instead of "seems" (though not always).
* "Seems" can be used when you get an impression via any of the physical senses, or from information received by any other means.
* "Look" may be used when the impression comes from sight, or from known facts, but not usually when it comes from other physical senses.
- I see black clouds in the sky — It seems it's going to rain // It looks as if it's going to rain.
- Share prices are falling — A market crash seems likely // A market crash looks likely.
- His voice is very nasal — It seems he has a cold // It sounds as if he has a cold.. [Not "It looks"] - The heating must be off — It seems cold in here // It feels cold in here.. [Not "It looks"]