Mostly, true (see about isotopes below).
Elements, by definition, are characterized by their atoms.
Generally, the same atoms - the same elements, different atoms - different elements.
Chemical element Hydrogen, for instance, consists of those and only those atoms that we call "Hydrogen atoms" consisting of one proton and one electron.
Any other atom is not present in the element we call Hydrogen.
Similarly, chemical element Iron consists of those and only those atoms that we call "Iron atoms" consisting of 26 protons, 26 electrons and 30 neutrons.
So, when talking about chemical elements, we assume that they are uniformly composed of the same atoms that are different from other atoms.
Slight complication exists with isotopes. These are different elements, but their composition is similar - they contain the same number of protons and electrons, but different numbers of neutrons. Chemically they are very much alike, so it's difficult to call them different chemical elements, but some other properties of these elements might be quite different.
For instance, Uranium has several major isotopes, all with 92 protons and 92 electrons, but different number of neutrons, it is 146 for Uranium-238 and 143 for Uranium-235.
So, from the chemical standpoint isotopes are practically indistinguishable, but some other their characteristics might be different.
The precise answer to this question depends on whether the word "element" is understood only in chemical sense (then chemically "the same" elements Uranium-235 and Uranium-238 have different atoms since the number of neutrons is different) or in absolute sense (then these two elements are different since some other properties are different).