Because of BGA have chlorophyll a similar to the green plants are photosynthetic autotrophs. And the cyanobacteria are unicellular, colonial or filamentous fresh water /marine terrestrial algae.

Introduction:
Cyanobacteria are often referred to as blue-green algae due to their ability to perform photosynthesis like algae and their blue-green pigmentation. However, it is important to note that cyanobacteria are not actually algae, but rather bacteria.

Explanation:
1. Classification:
Cyanobacteria belong to the phylum Cyanobacteria, which is a group of photosynthetic bacteria. They are classified as bacteria because they possess prokaryotic cell structure and lack membrane-bound organelles found in eukaryotic cells, such as algae.

2. Photosynthesis:
Cyanobacteria are capable of performing oxygenic photosynthesis, similar to algae and plants. They contain photosynthetic pigments, including chlorophyll-a and phycobilins, which allow them to capture sunlight and convert it into energy. This photosynthetic process is one of the reasons they are often called algae.

3. Habitat:
Cyanobacteria are found in various environments, including freshwater, marine, and terrestrial habitats. They can thrive in diverse conditions, ranging from extreme cold to hot deserts. Their ability to photosynthesize and produce oxygen makes them crucial contributors to the Earth's ecosystems.

4. Morphology:
Cyanobacteria exhibit a wide range of morphological forms, including unicellular, filamentous, and colonial structures. Some species possess specialized cells called heterocysts, which are involved in nitrogen fixation. Their diverse morphology allows them to adapt to different ecological niches.

5. Bacterial characteristics:
Despite their photosynthetic capabilities, cyanobacteria possess several characteristics that clearly distinguish them as bacteria rather than algae:
- They have prokaryotic cells with no defined nucleus or membrane-bound organelles.
- Cyanobacteria reproduce asexually, primarily through binary fission, which is a typical bacterial mode of reproduction.
- They possess a cell wall made of peptidoglycan, a characteristic feature of bacteria.

Conclusion:
In conclusion, cyanobacteria are called blue-green algae due to their photosynthetic abilities and pigmentation. However, they are fundamentally bacteria, belonging to the phylum Cyanobacteria. Their classification as bacteria is based on their prokaryotic cell structure, asexual reproduction, and possession of bacterial characteristics. Despite these distinctions, cyanobacteria are ecologically important organisms that contribute significantly to global oxygen production and nutrient cycling.