Base and Bottom

Base

The base is the lowest part of something, which supports it, like the foundation. We also use base figuratively to mean a group of people that support a political party or business.
Sarah planted flowers all along the base of the wall, so it would not be so ugly. This way, even if the wall blocks the view of the ocean, at least there are lovely flowers along its lower part.
When the politicians began their controversial speeches, journalists complained that they were not trying to say anything new or important, just repeating common slogans that were popular with their base.
When we use base for group of people that supports a political party or business, we often say party base and consumer base. A military base is a permanent military camp where soldiers can live and store supplies.
The company hired some new advertising agents, hoping to find a new ad campaign that might expand its consumer base and increase the number of people interested in their products.
Seoul is unique among major world cities in that it has a foreign military base in the centre of the city. The American military has been at the Itaewon base since the midtwentieth century.

Bottom

The bottom is the lowest part of something, or the part that is under the other parts. The bottom is not necessarily the base or the foundation because it does not always support the parts above it.
The Titanic was supposed to be the biggest and best ship of its day, but it sank. Now it's at the bottom of the sea.
Sarah had written a message on my coffee cup, but I couldn't find it. Finally I lifted the cup and looked at the bottom and there it was.
When someone tries to solve a mystery we say they are trying to get to the bottom of it.
After an hour of listening to strange noises in the garage, finally I got out of bed and went to look. When I opened the garage, I got to the bottom of all the noise—two raccoons were trapped inside.