"Having a crush on someone" is infatuation.  It's more common among teenagers and young people, especially with their first love. To fall in love is a more serious thing which may follow on from a crush, but not necessarily. Falling in love happens when you spend a lot of time with someone and come to appreciate them deeply, whereas crushes are ephemeral.  

"fall in love" and "have a crush on" are not fine terms of art which most people don't bother differentiating. The average native speaker would use them to express different situations quite naturally, without deep reflection.  In this forum, we analyse language more deeply in order to communicate the meaning but it's not a common preoccupation! 

I wish I could think of an older term for "crush" - there must have been one. It may be a term which expresses the spirit of the modern age - more introspective and fleeting.  An old-fashioned expression is "take a shine to" someone but that's just more become interested in someone - it's not as strong as crush.  Perhaps a better one would be "to have a thing for" someone, though that's not quite as serious as "to have a crush on". 

"crush" is a form of obsession. People still use that a lot - "he's obsessed with her". 

This link http://idioms.thefreedictionary.com/crush mentions "have a case on" which I've never heard of before.  It may be American.

<em>"I am not 100% sure what your question is."</em>
Michael, thank you! I'll try to make it more clear. Your words:

<em>"To fall in love is a more serious thing". </em>
<em>"Falling in love happens when you spend a lot of time with someone"</em>
<em>"and come to appreciate them deeply"</em>

I.e. you define 'to fall in love' in an opposition to a 'crush'. As it's deepest counterpart. Of course it happnes in lanuages: when a similar (or synonymous) word intervenes, the meaning of the opld one shift towars some exremity or 'niche'.

But: imagine a young person (16) who meet another young person at birthday party... and gets infatuated soon. Or falls in love... or develops a crush. The person doesn't analyse the feelings, he/she isn't a philosopher!:) Just feels something strong, which happens often with 16 years old people and less often with older people as well. May be the have seen each other only once, may be they has been dating for a week/two/month.

Now: how this situation would be called if
1) it isn't 2016 and the word 'crush' still isn't such common (many books we read we written well before 'to have crush on' become popular!) . Or, and mostly:
2) If we are avoiding slang expressions and prefers to stick to more romantic and literary language?

I know, there are people who love slang in such contexts... and there are people who would always awoid it (exactly in such contexts). I thought, they would use "to fall in love". 
But now i see your 'a lot of time', 'deeply', 'serious' and i'm confused.
Am I wrong?

In response to KP, I am not 100% sure what your question is.  I think you are saying that "have a crush on" is a slang form of "fall in love" and you are wondering why I am distinguishing their meanings.

They are definitely different in meaning, and not just in register.  "Have a crush on" is usually used for teenage infatuations.  It always refers to the period before a relationship starts.  This song captures the sense of "crush" quite well.

http://www.metrolyrics.com/crush-lyrics-jennifer-paige.html

"Falling in love" can happen with or without a formal relationship being agreed upon.  It's more unexpected and happens much more gradually than a crush. It doesn't have any sense of immaturity. This song captures the sense of "fall in love" quite well.

http://www.metrolyrics.com/suddenly-lyrics-billy-ocean.html

Michael, but how did people expressed the feeling more light and... how to say it.. teen-wise? ... than "when you spen a lot of time" and 'come to appreciate' and, interpretations besides (anyway, we all are unlikely to define 'love' correctly:)))) - more typical for what happens 'from the first sight' some 100 years ago?

Or how do they express it  now, when they need something more 'literary' (I don't know if I am right, but 'crush on' sounds a bit slangy for me, especially in the context of so basic human feeling)?

I have always been thinking that it would be 'fall in love' in these cases... (and wondered what do you say when you need to point at something deeper):/ Was I wrong here?


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<em>15.</em>
<em>Informal.</em>

<em>an intense but usually short-lived infatuation.</em>
<em>the object of such an infatuation: </em>

<em>Dictionary.com Unabridged</em>
<em>Based on the Random House Dictionary, © Random House, Inc. 2016</em>.

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<em>have a crush on someone</em>

<em>verb phrase</em>

<em>To be infatuated or enchanted with someone, esp to be secretly in love with someone older and more worldly than oneself (1913+)</em>
<em>The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D.</em>
<em>Copyright (C) 2007 by HarperCollins Publishers.</em>