Reconfigurable Intelligent Surface (RIS) can create favorable multipath to establish strong links that are useful in millimeter wave (mmWave) communications. While previous works used Rayleigh or Rician fading, we use the fluctuating two-ray (FTR) distribution to model the small-scale fading in mmWave frequency. First, we obtain the statistical characterizations of the product of independent FTR random variables (RVs) and the sum of product of FTR RVs. For the RIS-aided and amplify-and-forward (AF) relay systems, we derive exact end-to-end signal-to-noise ratio (SNR) expressions. To maximize the end-to-end SNR, we propose a novel and simple way to obtain the optimal phase shifts at the RIS elements. The optimal power allocation scheme for the AF relay system is also proposed. Furthermore, we evaluate important performance metrics including the outage probability and the average bit error probability. To validate the accuracy of our analytical results, Monte-Carlo simulations are subsequently conducted to provide interesting insights. It is found that the RIS-aided system can achieve the same performance as the AF relay system with low transmit power. More interestingly, as the channel conditions improve, the RIS-aided system can outperform the AF relay system having the same transmit power with a smaller number of reflecting elements.