Does taking a shower have the same effect on muscles as warming up?
Hot shower will definitely affect your muscles health. Hot water shower results in Vasodilation,which will decrease the vascular resistance and allows blood to flow easily through the blood vessels. As the vasodilation (increase in diameter of blood vessels) allows blood to move without resistance and which in turn nourish the tissues with sufficient oxygen and nutrients. Also it affects in the removal of metabolic wastes from cells. There is another process called  Vasoconstriction (decrease in blood vessel diameter) which makes the blood vessels to contract and may lead to increased blood pressure.

There is a technique called as Heat therapy which will be effective in muscle and body health.


  Heat therapy, also called thermotherapy, is the use of heat in
  therapy, such as for pain relief and health. It can take the form of a
  hot cloth, hot water, ultrasound, heating pad, hydrocollator packs,
  whirlpool baths, cordless FIR heat therapy wraps, and others. It can
  be beneficial to those with arthritis and stiff muscles and injuries
  to the deep tissue of the skin. Heat may be an effective self-care
  treatment for conditions like rheumatoid arthritis.
  
  Heat therapy is most commonly used for rehabilitation purposes. The
  therapeutic effects of heat include increasing the extensibility of
  collagen tissues; decreasing joint stiffness; reducing pain; relieving
  muscle spasms; reducing inflammation, edema, and aids in the post
  acute phase of healing; and increasing blood flow. The increased blood
  flow to the affected area provides proteins, nutrients, and oxygen for
  better healing.Reference


While taking a hot water bath we are just making our muscles and tissues nourished, which means the muscles will be in a healthy state for expansion and contraction. So it is recommendable to take a hot bath before exercising.