The alphabet that we use in English is sometimes called the Roman alphabet. Romanized Sanskrit is the general term for any Sanskrit text that is written in the Roman alphabet.
Romanized Sanskrit became popular among Western scholars when they encountered Sanskrit for the first time, and it became more established in the 19th century. But even though that era has long passed, romanized Sanskrit is still often used today. This is for a few reasons:
If you can read Roman letters already, it's easy to learn and read romanized Sanskrit.
Romanized Sanskrit doesn't lose any information. That is, we can always convert it back to Devanagari or another script.
Romanized Sanskrit is often easier to use with computers.
Today, it is easier than ever to display Sanskrit in Devanagari or another Indian script. But even so, it is useful to know about romanized Sanskrit and how to use it.
The International Alphabet for Sanskrit Transliteration, or IAST for short, became common among Western scholars in the 19th century.
ISO-15919 is the modern standard for romanizing all Indian languages, including Sanskrit. ISO stands for the International Standards Organization, and 15919 is a numeric code associated with the standard.
IAST and ISO-15919 are largely similar. But they differ in a few letters: