I am trying to understand how AES is comparable to GOST
Except for them both being block ciphers, and relying on similar components (e.g. sboxes), there is actually very little similar to how they work internally.
GOST (Magma, as Squeamish points out, GOST is a fairly generic term) is a fairly straight forward Feistel cipher internally, where the block being operated on is split into two halves, and then one half is modified (based on the other half and the key); this is done 32 times. Decryption is done by performing the cipher, but with an inverted key schedule.
AES, in contrast, is a Substitution/Permutation cipher; each round (except the last, which is slightly different) can be viewed as the concatenation of four operations, each of which operates on the entire block. Decryption can be viewed as performing each of these suboperations in reverse (as each one is invertible).
Like for parameters such as Bit shifting
AES doesn't have any explicit 'bit shifts'. Now, one of the suboperations is called MixCollumns; in the forward direction, it involves a Galois multiply of the elements by 1, 2 and 3; I suppose you could look at multiplying by 2 and 3 as 'kind of' bit shifting, but that's a strained comparison IMHO.
addition of the subkey to the input
Magma stirs in the subkey by xoring the input to the sbox (which affects the other side). In contrast, AES xor's the subkey into the entire block.
how S-BOX application in AES is different than GOST?
Magma uses the sboxes (8 different 4 bit to 4 bit sboxes) as a part of the Feistel function (to select the value that affects the other side). In constrast, as one of the suboperations, AES applies the (single 8 bit to 8 bit sbox) sbox individually to each byte of the block (which implies that the AES sbox must be invertible).
Why swapping of halves is not required in AES?
Because AES is not a feistel network. Magma swaps halves, to make decryption easier (so that the decryption operation is precisely the same as the encryption operation, except that the key schedule is reversed). AES uses a different method for doing decryption, and so it has no reason to swap halves.