In asymmetric cryptography you always deal with key-pairs. For each secret key there is a corresponding public key. So to answer your first question: yes, the public key of a primary key pair is different from the public key of its subordinate key pair.
I tried to reproduce your experiment and created a GnuPG test key with a primary key (ID 0xA6271DD4) and a subordinate key (ID 0x5336E1DC). I then exported the subordinate key to a file and checked, which packets it contains.
$ gpg --export-secret-subkey 5336E1DC! > subkey.gpg $ gpg --list-packets subkey.gpg | grep "\(packet\|keyid\)" :secret key packet: keyid: 877AA505A6271DD4 :user ID packet: "testtest <test@test>" :signature packet: algo 1, keyid 877AA505A6271DD4 :secret sub key packet: keyid: B0389BEB5336E1DC :signature packet: algo 1, keyid 877AA505A6271DD4 $
Please note that both the user ID and the secret subordinate key are signed by the primary key. On the first look it seems that both the primary and subordinate secret key were exported. Show more info about the first secret packet.
$ gpg --list-packets subkey.gpg | head # off=0 ctb=95 tag=5 hlen=3 plen=277 :secret key packet: version 4, algo 1, created 1546169910, expires 0 pkey[0]: [2048 bits] pkey[1]: [17 bits] gnu-dummy S2K, algo: 0, simple checksum, hash: 0 protect IV: keyid: 877AA505A6271DD4 # off=280 ctb=b4 tag=13 hlen=2 plen=20 :user ID packet: "testtest <test@test>" $
When exporting a secret key in GnuPG, the corresponding public key is always exported with it. So this secret key packet contains a public key of 2048 bits plus probably its 17 bits hash. But the secret key itself is missing, only a stub was exported: gnu-dummy S2K, algo: 0, simple checksum, hash: 0. To wrap it up: When exporting a secret sub key, you always export the public sub key and the public primary key (necessary to verify the signatures) with it.
You write that your public sub key has fewer lines than your public master key. I was not able to reproduce that. With GnuPG you can export a public key without any of its subkeys, in the example above by the command gpg --export A6271DD4! > pubkey.gpg (please note the exclamation mark). On the other hand, it is not possible to export just a public sub key. But if comparing a master key with a master key plus its sub key, the latter one naturally has more lines. So to better understand your observation it would be good to know the exact commands you used.