Create RSA 1024 key pair using openssl

but why do these two files have different sizes (608 bytes and 162 bytes)? the RSA 1024 key pair must be the same size, right?

There are two formats for the private key (see, for example, PKCS # 1 or RFC 3447).

OpenSSL uses a second representation which can be described as a "long form" a n, e, d dp, dqetc.

$ openssl pkey -in test-key.txt -inform PEM -text
-----BEGIN PRIVATE KEY-----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-----END PRIVATE KEY-----
Private-Key: (1024 bit)
modulus:
    00:c4:05:bb:27:9b:f3:2f:8b:a2:ca:b7:d3:10:63:
    83:71:23:6d:37:5b:f8:27:5d:95:96:7e:25:05:b1:
    8e:b8:64:26:c9:4b:37:b5:2c:c4:bf:37:43:3d:19:
    35:84:71:19:6e:4f:77:54:43:51:f9:aa:58:06:26:
    e7:16:53:85:11:68:cf:bb:1e:11:0d:32:21:f5:67:
    a0:8f:ce:94:3b:b3:c7:e6:db:f1:c8:b7:b5:21:90:
    29:00:cf:1e:fe:5a:3b:c8:dd:a1:e0:6d:3f:4a:33:
    f1:9a:20:a0:d0:6e:55:e4:40:4e:71:e4:0a:8a:1c:
    ad:dd:2f:c2:ea:fe:c5:6a:19
publicExponent: 65537 (0x10001)
privateExponent:
    64:88:bb:f0:18:9f:a4:e6:ec:db:23:64:70:a7:59:
    26:91:90:d6:2f:a9:1a:27:79:2c:f2:0d:72:da:19:
    e4:a0:18:f4:6c:4b:69:f4:48:03:fa:07:d6:32:33:
    ac:75:85:21:7a:48:2d:43:49:ab:ce:9d:ce:a9:ed:
    23:1a:3a:c8:48:4a:02:88:aa:e2:bf:69:97:03:69:
    a7:94:f5:29:ba:54:3a:55:13:11:0c:28:ae:a1:fa:
    11:0b:d9:06:f2:1b:f3:43:1f:9a:6e:64:6b:fd:ec:
    69:1a:f5:c6:27:69:24:22:d4:c8:b7:a3:c4:52:71:
    27:a5:cb:52:13:cd:7d:b1
prime1:
    00:f5:4f:5c:ad:d1:e7:a2:4c:31:1a:f2:93:07:2d:
    f1:1b:0a:2b:1e:e2:89:5f:97:e5:1d:73:cc:d6:48:
    7a:53:f3:78:b9:ad:ee:1d:72:d5:79:3f:7c:fd:b6:
    31:57:90:0d:fc:57:bd:09:23:74:6e:47:38:ab:97:
    0f:76:b8:78:a3
prime2:
    00:cc:90:86:44:46:3f:e5:97:a1:2a:57:13:da:09:
    e6:6e:3a:26:0d:72:65:57:20:4a:b7:4f:74:d1:6e:
    36:31:37:6c:c1:21:d0:c1:13:d1:6a:d7:d6:56:fd:
    80:5e:f3:53:3c:01:57:a0:c5:6b:ba:9b:35:b8:d2:
    bf:5b:93:12:13
exponent1:
    77:5b:f6:2c:5d:45:e7:a2:4b:02:61:a5:48:89:02:
    17:b6:0a:e5:2c:34:cb:5e:8d:0c:97:9b:c3:67:e0:
    9d:98:89:d5:4e:db:dd:58:52:a6:7c:4d:c4:e5:31:
    7c:f9:8a:d4:8d:9c:5d:25:f3:30:f5:56:8d:a7:22:
    cf:11:53:21
exponent2:
    03:41:6d:91:9a:98:9b:bb:cd:09:d2:76:f3:6a:62:
    eb:70:2b:78:dd:50:35:91:c2:fe:a5:da:13:17:30:
    ef:99:95:36:81:a6:43:dc:5f:e1:d6:6b:87:d8:e2:
    f9:1f:e0:3c:3d:3d:3a:c6:c9:8f:1f:b7:3c:28:c6:
    78:db:9f:57
coefficient:
    32:1b:c3:66:90:b2:01:b3:87:1f:90:3b:7a:a9:e2:
    cc:90:14:88:d5:32:de:eb:6f:da:5d:90:1d:22:19:
    16:2a:a1:fb:8d:a8:4e:0b:36:f8:02:21:da:3f:11:
    9f:fe:47:08:32:db:cb:47:0e:49:34:13:8b:48:51:
    93:24:1a:1c

is it a pem format?

Yes:

$ openssl genrsa -out privatekey.txt 1024
$ cat privatekey.txt 
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----

-----BEGIN RSA PRIVATE KEY-----and -----END RSA PRIVATE KEY-----indicate that the key is in PEM format.

-----BEGIN XXX----- -----END XXX----- , DER.

RSA* rsa = RSA_new();
BN_hex2bn(&rsa->n, WHAT_HERE);
BN_hex2bn(&rsa->e, AND_WHAT_HERE);
RSA_public_encrypt(....);

PEM_read_PrivateKey, PEM_read_PupblicKey , PEM. , pem(3) OpenSSL.

OpenSSL . , cd <openssl dir>/apps :

openssl-1.0.1f/apps$ grep -R PEM_read *
apps.c:     x=PEM_read_bio_X509_AUX(cert,NULL,
apps.c:     pkey=PEM_read_bio_PrivateKey(key,NULL,
apps.c:     rsa = PEM_read_bio_RSAPublicKey(key, NULL, 
apps.c:     pkey=PEM_read_bio_PUBKEY(key,NULL,
ca.c:   if ((req=PEM_read_bio_X509_REQ(in,NULL,NULL,NULL)) == NULL)
cms.c:          cms = PEM_read_bio_CMS(in, NULL, NULL, NULL);
cms.c:          rcms = PEM_read_bio_CMS(rctin, NULL, NULL, NULL);
crl2p7.c:           crl=PEM_read_bio_X509_CRL(in,NULL,NULL,NULL);
crl.c:      x=PEM_read_bio_X509_CRL(in,NULL,NULL,NULL);
dh.c:       dh=PEM_read_bio_DHparams(in,NULL,NULL,NULL);
dhparam.c:              dsa=PEM_read_bio_DSAparams(in,NULL,NULL,NULL);
dhparam.c:              dh=PEM_read_bio_DHparams(in,NULL,NULL,NULL);
dsaparam.c:     dsa=PEM_read_bio_DSAparams(in,NULL,NULL,NULL);
ec.c:           eckey = PEM_read_bio_EC_PUBKEY(in, NULL, NULL, 
ec.c:           eckey = PEM_read_bio_ECPrivateKey(in, NULL, NULL,
ecparam.c:      group = PEM_read_bio_ECPKParameters(in,NULL,NULL,NULL);
gendsa.c:   if ((dsa=PEM_read_bio_DSAparams(in,NULL,NULL,NULL)) == NULL)
genpkey.c:  pkey = PEM_read_bio_Parameters(pbio, NULL);
nseq.c:     while((x509 = PEM_read_bio_X509(in, NULL, NULL, NULL))) 
nseq.c: if (!(seq = PEM_read_bio_NETSCAPE_CERT_SEQUENCE(in, NULL, NULL, NULL))) {
pkcs12.c:   while((cert = PEM_read_bio_X509(in, NULL, NULL, NULL))) {
pkcs7.c:        p7=PEM_read_bio_PKCS7(in,NULL,NULL,NULL);
pkcs8.c:            p8inf = PEM_read_bio_PKCS8_PRIV_KEY_INFO(in,NULL,NULL, NULL);
pkcs8.c:            p8 = PEM_read_bio_PKCS8(in, NULL, NULL, NULL);
pkeyparam.c:    pkey = PEM_read_bio_Parameters(in, NULL);
req.c:          req=PEM_read_bio_X509_REQ(in,NULL,NULL,NULL);
req.c:      param = PEM_read_bio_Parameters(pbio, NULL);
req.c:          x = PEM_read_bio_X509(pbio, NULL, NULL, NULL);
s_client.c:     sess = PEM_read_bio_SSL_SESSION(stmp, NULL, 0, NULL);
sess_id.c:      x=PEM_read_bio_SSL_SESSION(in,NULL,NULL,NULL);
smime.c:            p7 = PEM_read_bio_PKCS7(in, NULL, NULL, NULL);
s_server.c: ret=PEM_read_bio_DHparams(bio,NULL,NULL,NULL);
s_server.c:     if (PEM_read_X509(in,&x,NULL) == NULL)
x509.c:     req=PEM_read_bio_X509_REQ(in,NULL,NULL,NULL);

apps , genrsa, x509, req, encrypt, decrypt ..