They are somewhat parallel, but not the same idea. "Landrace" usually refers specifically to domesticated plants or animals, and indicates a traditional or 'heirloom' variety developed (usually over a long time) in and and originally limited to a specific region. "Ecotype" refers to a locally adapted population or populations that is, in its local adaptation, genetically distinct from the rest of the species; the local adaptation is assumed to be a result of the action of natural selection. Ecotype is used more generally for non-domesticated organisms. A landrace might be considered a special case of an ecotype (within a domesticated organism) IF what makes it distinct from other varieties is also distinctly adaptive to local conditions (which may or may not be the case).
They are somewhat parallel, but not the same idea. "Landrace" usually refers specifically to domesticated plants or animals, and indicates a traditional or 'heirloom' variety developed (usually over a long time) in and and originally limited to a specific region. "Ecotype" refers to a locally adapted population or populations that is, in its local adaptation, genetically distinct from the rest of the species; the local adaptation is assumed to be a result of the action of natural selection. Ecotype is used more generally for non-domesticated organisms. A landrace might be considered a special case of an ecotype (within a domesticated organism) IF what makes it distinct from other varieties is also distinctly adaptive to local conditions (which may or may not be the case).
I agree with what was said above, but also expand to say that landraces are often associated with artificial selection and breeding, and ecotypes are associated with natural selection.
A similar question "What is the exact difference between ecotype and chemotype of plant species?" was asked by Ammar Bader of Umm Al-Qura University. Several experts shared their views and I suggest you to check these responses for a plausible answer to your query.
An ecotype is a wild plant that has historically occured in one area, and over time has become adapted to that specific area (soil type, climate, altitude etc). A landrace is the same, except it has also been cultivated by farmers and become domesticated.
A landrace is essentially a domesticated ecotype. Landraces will typically be more distinct from wild populations than ecotypes for this reason, they have two selection pressures (one natural and one artificial) where as ecotypes only have natural selection.
To the best of my knowledge, cultivar is a cultivated variety developed from wild plants or cultivated plants through conventional or modern plant breeding techniques. Some botanists feel that the term cultivar is not technically correct, therefore should not be used (see the attached document). A variety has 2 meanings. A genotype developed through plant breeding techniques and released for commercial cultivation after several field trials is generally regarded as a variety. In botanical binomial nomenclature if there are 2 identical genotypes differing slightly belonging to the same species they are designated as varieties for e.g plamarosa (Cymbopogon martinii var. motia) and ginger grass (Cymbopogon martinii var. sofia) or Mentha arvensis var. piperascence.