Why do places on the same lines of latitude have different temperatures?
There are many things that determine the temperature of a location on earth, latitude being one of the major ones. Local temperature differences, within the same latitude, would mainly be caused by movement of areas of high and low air pressure or changes in elevation (think about snow-capped mountain peaks when it is 80 degrees Fahrenheit at the base of the mountain). Places near oceans or other large bodies of water will also see temperature influences from air movement from either colder or warmer water.
Temperature differences of larger areas at greater distances (climate) , along the same latitude, are usually caused by either major air currents like the Jet Stream or major ocean currents like the Gulf Stream. There are similar air and water currents found all over the world. They can cause either warmer or colder temperatures (for that latitude). Other things that can have major influences are the ability of the ground to warm and then release stored heat (light colored, dry, sandy soils warm the air during the day but release their heat very quickly at night, while moist wet soil with lots of vegetation will warm more slowly in the morning but also release heat more gradually at night).
Other things that may influence temperatures to a lesser degree are things like air pollution, atmospheric volcanic ash; even algae growth has been shown to have effects on temperature.
Latitude describes the north and south position on the earth. You can have two places on similar latitude with significantly different average temperature and seasons. A good example is Duluth Minnesota in the US at 46 degrees north, and Paris France in Europe at 48 degrees north. While Duluth consistently gets cold winters with significant snowfall, Paris rarely gets cold enough for snow.
There are many factors that lead to temperature variations. They are primarily related to movement of air pressure known as jet-streams. Proximity to a coast is another big factor. Places near the ocean are affected by the air moving over the water be it warmer or cooler.