Basically there are two types of Supernovae (SN), Type I and Type II. Type I have no Hydrogen emission lines in their spectrum and Type II do.
But it is actually a bit more complicated and the names are largely historic as often in astronomy. In this case it is because of the significant improvement in spectroscopy with which the chemical composition of the remnants can be analysed.
It has now been realised that we must distinguish in fact three different type I supernovae, now labelled IA, IB, and IC. Only type IA SN’s are caused by the explosion of a White Dwarf star in a binary system when it exceeds the Chandrasekhar limit. It is characterised by the presence of Silicon absorption lines in the spectrum.
The others, type IB and IC are like type II, the result of a core collapse of a giant star. The difference between these core-collapse SN classes are related to whether they have Hydrogen and Helium in their spectra.
Type IB has Helium in its spectrum because the exploding star has retained its Helium envelope, but no Hydrogen. Type IC lacks Helium in its spectrum and has lost both its Hydrogen and Helium envelopes prior to the explosion. Type II supernovae have both Hydrogen and Helium in their spectrum.
Accurate spectra can be best obtained when the supernova is at its brightest. Sometimes SN spectra change over time and thus appear to change type. This is understood to be caused by the expanding material catching up with envelopes of previously ejected material.
It is even more complex
Modern research increasingly blurs the distinction between Type II and Type Ib and Ic supernovae. Key aspects of modern observations are to observe the transient events in many different parts of the EM-spectrum (especially X-ray and Radio frequencies are very important) and to try to detect these events as early as possible, preferably before the main outburst (image).
Observatories such as PANSTARRS (Panoramic Survey Telescope and Rapid Response System located at Haleakala Observatory in Hawaii), and the Zwicky Transient Facility, a 47 square degree field of view telescope at Mount Palomar are providing early response observations.
One of the latest discoveries (since date of this publication) is the AT2018cow supernova, observed in June 2018 and dubbed “the cow”, that has baffled astronomers. It is both very luminous and very short lived and the jury is still out on the precise nature of this event.