There are very few similarities between elements, compounds and mixtures. At the most basic level, all the three are composed of atoms. Elements and compounds are purely homogeneous substances and they have a constant composition throughout. Elements and compounds cannot be separated into their respective constituents by physical means. Compounds and mixtures are made up of different elements or different atoms.
There are a number of differences between the three types of substances.
Elements are composed of only 1 type of atoms and any subdivision can only result in same element. All the atoms of an element have the same properties (assuming they are the same isotope). Some examples are iron, magnesium, gold, etc.
Compounds are composed of two or more elements in a fixed ratio. The properties of a compound are different from that of its individual constituents. A compound can be broken down into its constituents. Some examples of compounds are sodium chloride (common salt), water, etc.
A mixture is composed of two or more elements or compounds in a non-fixed ratio. All the constituents of a mixture retain their properties. A mixture can be divided into constituents by physical means. An example of a mixture is trail mix.
Hope this helps.