Encryption vs. decryption of same plaintext
It very much depends on the encryption scheme you are using.
In a deterministic encryption scheme, the same plaintext is always encrypted to the same ciphertext (when using the same key of course).
This indeed causes a security problem for all deterministic schemes. I.e. no deterministic scheme can be IND-CPA secure.

If you take a look at the IND-CPA game, you can see why: The adversary $\mathcal{A}$ may simply choose two random messages $m_0,m_1$ and submit them to the challenger. After receiving the ciphertext $c$ he asks for an encryption of $m_0$ and receives ciphertext $c'$. Now as the scheme is deterministic, it follows that $c=c'$ if and only if $c$ is an encryption of $m_0$, therefore if $c=c'$ $\mathcal{A}$ outputs $0$, otherwise $1$.

Therefore, to achieve IND-CPA security we need probabilistic encryption. In a probabilistic encryption scheme, the encryption algorithm uses additional randomness to produce the ciphertext. See for example ElGamal encryption, where the ciphertext consists of two parts, one of which is a random group element. Also all secure modes of operations for block-ciphers introduce randomness in the form of nonces or initialization vectors.

An important thing to note about probabilistic encryption is that, because decryption must be deterministic, and a single plaintext corresponds to a larger number of ciphertexts, the ciphertext will always be longer than the plaintext.