First of all, I'd try to clear up if it wasn't all just a misunderstanding. It sounds like the two boys are friends, and the mums are friends, and the mums both know that the boys are friends. It seems unlikely that your DS wouldn't be invited, unless there was a good reason, in which case I would have expected the mum to approach you in a 'I'm really sorry, I know our boys are friends and would have loved to invite him but because of x we couldn't this time' way, and maybe suggest a playdate between the two of them instead.
So, chances are the invite got lost in a school bag or something. And the other mum is now wondering why you are not RSVPing and refusing to mention the party when you talk.
I hate confrontation but I think you can ask her about this. If your DS wasn't invited for 'mean' reasons, then asking her will put her on the spot - but not undeservedly so.
Even if it doesn't turn out to have been a mistake, you may learn WHY your DS wasn't invited. And that info can help inform your reaction, and also how you explain it to your DS.
For example if it turns out that the mum really thought your DS should be invited, but for some reason - maybe the boys had a falling out on the day the invites were decided - the boy didn't want to, and mum failed to convince him, and didn't want to override his wishes.
-> I think you can continue being friends with the mum. She didn't do anything majorly wrong, it was just bad luck/timing. Though she might have approached you to explain.
-> You can explain to your DS 'remember, a little while back, when you had that falling out with other boy' and that sometimes people react in a hurtful way when they are feeling hurt themselves. Perhaps your DS wouldn't have invited the other boy either, if he'd had had to decide on exactly that day? But just because other boy 'lashed out' so to say, on that day, doesn't mean that you can't try to make up (perhaps they have already) and continue being friends.
If, as another example, it turns out your DS wasn't invited because the party is taking place at a place of which the other mum knows your DS wouldn't want to go (e.g. it's too loud, noisy, overwhelming, scary)
-> Again, you can stay friends with the mum. Suggest that she could have avoided some hurt by inviting your DS, who'd then decline, and the place could be offered to someone else.
-> You can explain to your DS that the other boy really wanted him to be at his party but knew that DS wouldn't enjoy that kind of party.
You ask how you can explain this to your son, I say you have to know the reasons before you can explain them.
If you really don't want to politely ask the other mum, then I'd go with benign reasons. 'I really don't know but it could be all manner of things. Perhaps you two had a big fall-out on the day the invites went out? The other boy may have changed his mind soon after, as you two made up, but couldn't change the invites any more. Or perhaps ...'
Failing knowledge of the reasons, I would NOT assume hurtful reasons. It would be a shame to lose this friendship due to unspoken assumptions that may be totally unfounded.
I have to say though that there is a boy in my DS' school who can be a bit of a bully. Many children want to be friends with this boy - he is very manipulative, gives gifts, includes, just to then turn on his 'best friend' to be very hurtful and excluding. This boy explicitly uses party invites to manipulate and exclude. My own DS thought for a while that this boy was his best friend, however it turned out that this boy was just manipulating him. DS wasn't invited to this boys party (and was constantly told so: 'I'm inviting everyone, but not you, nananeenana'). DS still wanted to invite this boy to his, thinking he was his friend, or maybe that by making a gesture the boy would be less mean to him. At which point I put my foot down and vetoed. Having observed that every single time they had both been at the same parties, it had ended with DS in tears due to this boy. He didn't need that at his own party.
That boy's mum is nice enough, and we are polite to each other, but not friends.
What I'm saying is, if your boy is not particularly on the ball with regards to social going ons, it is entirely possible that the other boy has been manipulating him, and that they never really were friends, but your DS was lead on.
If that is the case, by all means stop being friends. But don't assume this is the case, when it may all be very benign!