What is the difference between /a/ and /æ/?

Solution 1:

There are many different ways of writing English phonetically. Linguists and people interested in language (such as you often find on this site) often use the International Phonetic Alphabet (IPA) system.

According to that system, the vowel sound in add is written /æ/.

Google's transcription isn't incorrect, it just doesn't use IPA symbols.

Google, of course, isn't a dictionary. It outsources those tasks, and then, for some reason, integrates the information into its search results in such a way that it appears to be Google's information.

Beneath the "Dictionary" box that they display, there's a link that says, "From Oxford", which takes you to the Lexico website. This site appears to use the New Oxford American Dictionary transcription method, or "NOAD" in this list: Traditional respelling systems

If you look at that handy chart, you'll see that IPA's "æ" corresponds to NOAD's "a"

Solution 2:

Unfortunately, I managed already to lose access to the account from which I posted this question. Since new accounts can't comment, I can only reply to @Juhasz by adding an answer. I understand that this is not what answers are for, but, unfortunately, this is currently my only option.

I don't think Google uses the NOAD system, since it doesn't, say, use /ē/ or /ä/ in its transcriptions. According to this page, Lexico doesn't use /æ/ for its UK dictionary at all. All other symbols, however, appear to be the same as they are in the IPA. I find this rather weird. Searching for 'aid' gives /eɪd/, by the way.

The US dictionary entry gives "/ad/ /æd/" as transcriptions, but the UK dictionary entry only gives "/ad/". This probably means that google uses the transcription from the UK dictionary, despite linking to the US counterpart.

It seems tempting to assume that /æ/ and /a/ are two symbols representing the same sound, but according to the IPA Vowel chart that LPH linked to, this isn't the case. Could it perhaps be that /æ/ isn't used in RP?

I'm still rather confused which sound best fits words such as 'add' or 'cat' pronounced in RP, but /a/ seems more like how I pronounce it. Even though Cambridge gives /æd/ as the transcription, the audio sounds more like /ad/ to me.