When the Spanish came to the Philippines, they found in use the baybayin, a native writing system, that was an abjad or a consonant writing system. The baybayin was still in its early stages of development as a writing system, lacking symbols for all the vowel sounds of the various Philippine dialects and not yet totally uniform in appearance across varying geographic regions.
The Philippine Baybayin is one of a dozen or so individual alphabets from such Southeast asian islands as Sumatra, Java, and Sulawesi which are derived from ancient India and share the Sanskrit characteristic that any consonant is pronounced with the vowel a following it… (this vowel occurs with greatest frequency in Sanskrit, and also probably in all Philippine languages. (Source: Baybayin at Wikipedia.com)
Other earlier writing systems around the world, that started out as abjad, evolved to create letters to include all vowels within their corresponding languages. Many times, development of these abjads to complete alphabetic systems came from outside influences. The Greek alphabet, for example, evolved to accommodate vowels. The Greek alphabet was a direct successor of Phoenician, another abjad.
So it is not suprising, that when the Spanish came, chroniclers attempted to alter the baybayin abjad symbols with diacritical marks or glyphs in order to incorporate all the various vowel sounds of the locals’ language.
“Baybayin” means the act of spelling in Pilipino. That is what the Filipinos called it when the Spanish came, but later, around 1914, Paul Versoza had travelled to the United States and had been lecturing there on “Tagalog philology, calligraphy, and linguistics”. He published a book and, to talk about baybayin to the Western world, coined the word “alibata” after the Arabic letters of alif, ba, ta, even if the baybayin had no Arabic influences. (Also see Pangbansang Titik nang Pilipinas – baybayin.com)
I myself prefer to use the original word of “baybayin” and the abjad or original baybayin symbols without the glyphs.