In simple words: A filter detects a kind of local pattern; a feature map shows where it appears.
The filter
A kernel or filter is a small grid of numbers. It moves across the image and calculates a new value at each position. The filter values are learned during training.
The result
The resulting grid is called a feature map. It shows where a particular learned pattern appears strongly. Many filters create many feature maps, capturing different clues.
See the flow
image patch × filter→value→feature map
Simple example
One filter may highlight horizontal edges; another may respond to corners. Later layers combine both.
Remember: A filter detects a kind of local pattern; a feature map shows where it appears.