There are two things obfuscating what's going on here:
POSTMAN follows redirects on GET requests but doesn't provide information on the request history (e.g. if I say GET URL1 and am redirected to GET URL2, it just tells me about my original GET URL1, even though it provides the results of GET URL2)
The cURL example in the documentation contains a -L flag which tells cURL to follow redirect. cURL isn't known for providing any information outside of what's explicitly asked for, and this is another case of that.
If you want to see what's actually going on, you can put cURL in verbose mode by adding the 'v flag and see everything that happens, e.g.:
curl -v -L https://api.box.com/2.0/files/FILE_ID/content -H "Authorization: Bearer TOKEN"
* About to connect() to api.box.com port 443 (#0)
* Trying 74.112.184.225...
* connected
* Connected to api.box.com (74.112.184.225) port 443 (#0)
* SSLv3, TLS handshake, Client hello (1):
* SSLv3, TLS handshake, Server hello (2):
* SSLv3, TLS handshake, CERT (11):
* SSLv3, TLS handshake, Server finished (14):
* SSLv3, TLS handshake, Client key exchange (16):
* SSLv3, TLS change cipher, Client hello (1):
* SSLv3, TLS handshake, Finished (20):
* SSLv3, TLS change cipher, Client hello (1):
* SSLv3, TLS handshake, Finished (20):
* SSL connection using RC4-SHA
* Server certificate:
* subject: serialNumber=ts5jamwzcjWP0oTyh2m74yh0zsB2zyOR; C=US; ST=California; L=Palo Alto; O=Box.net, Inc.; CN=*.box.com
* start date: 2011-09-27 22:07:27 GMT
* expire date: 2013-09-29 11:02:11 GMT
* subjectAltName: api.box.com matched
* issuer: C=US; O=GeoTrust, Inc.; CN=GeoTrust SSL CA
* SSL certificate verify ok.
> GET /2.0/files/5620199214/content HTTP/1.1
> User-Agent: curl/7.24.0 (x86_64-apple-darwin12.0) libcurl/7.24.0 OpenSSL/0.9.8r zlib/1.2.5
> Host: api.box.com
> Accept: */*
> Authorization: Bearer TOKEN
>
< HTTP/1.1 302 Found
< Server: nginx
< Date: Sun, 17 Mar 2013 20:48:40 GMT
< Content-Type: text/html; charset=utf-8
< Connection: keep-alive
< Cache-control: no-cache, no-store
< Location: https://www.boxcloud.com/bc/1/b4c1b5e872bf843d3ded7bcae5f4f175/2Of-pgQHiFlfW6KldVyHAxtUIEW0l7HoOpi14-VGcxcSnn2CtobCO1UjJZLI58w_oCTNcPMKbUR_gn-ncDkAbw,,/f9a04d69f716d92ceebd848bb9ccded8/
< Content-Length: 0
<
* Connection #0 to host api.box.com left intact
* Issue another request to this URL: 'https://www.boxcloud.com/bc/1/b4c1b5e872bf843d3ded7bcae5f4f175/2Of-pgQHiFlfW6KldVyHAxtUIEW0l7HoOpi14-VGcxcSnn2CtobCO1UjJZLI58w_oCTNcPMKbUR_gn-ncDkAbw,,/f9a04d69f716d92ceebd848bb9ccded8/'
* About to connect() to www.boxcloud.com port 443 (#1)
* Trying 74.112.184.74...
* connected
* Connected to www.boxcloud.com (74.112.184.74) port 443 (#1)
* SSLv3, TLS handshake, Client hello (1):
* SSLv3, TLS handshake, Server hello (2):
* SSLv3, TLS handshake, CERT (11):
* SSLv3, TLS handshake, Server finished (14):
* SSLv3, TLS handshake, Client key exchange (16):
* SSLv3, TLS change cipher, Client hello (1):
* SSLv3, TLS handshake, Finished (20):
* SSLv3, TLS change cipher, Client hello (1):
* SSLv3, TLS handshake, Finished (20):
* SSL connection using RC4-SHA
* Server certificate:
* subject: serialNumber=o2MxwjKDoF9mEZ3YNhBMR/WISRBUXT6b; C=US; ST=California; L=Palo Alto; O=Box, Inc.; CN=*.boxcloud.com
* start date: 2012-02-27 00:10:39 GMT
* expire date: 2014-03-01 01:48:45 GMT
* subjectAltName: www.boxcloud.com matched
* issuer: C=US; O=GeoTrust, Inc.; CN=GeoTrust SSL CA
* SSL certificate verify ok.
> GET /bc/1/b4c1b5e872bf843d3ded7bcae5f4f175/2Of-pgQHiFlfW6KldVyHAxtUIEW0l7HoOpi14-VGcxcSnn2CtobCO1UjJZLI58w_oCTNcPMKbUR_gn-ncDkAbw,,/f9a04d69f716d92ceebd848bb9ccded8/ HTTP/1.1
> User-Agent: curl/7.24.0 (x86_64-apple-darwin12.0) libcurl/7.24.0 OpenSSL/0.9.8r zlib/1.2.5
> Host: www.boxcloud.com
> Accept: */*
> Authorization: Bearer TOKEN
>
< HTTP/1.1 200 OK
< Server: nginx
< Date: Sun, 17 Mar 2013 20:48:41 GMT
< Content-Type: image/png
< Content-Length: 15039
< Connection: keep-alive
< Cache-control: private
< Accept-Ranges: bytes
< Content-Disposition: attachment;filename="Screenshot_1_14_13_5_33_PM.png";filename*=UTF-8''Screenshot_1_14_13_5_33_PM.png
< X-Content-Type-Options: nosniff
< Accept-Ranges: bytes
<
?PNG
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