BIP39 (Bitcoin Improvement Proposal) describes the implementation of a mnemonic sentence (set of easy to remember words from a predefined wordlist of 2048 words) that can be mapped to a binary seed from which you get a master key which in turn is used as per BIP32 for the generation of deterministic wallets.
SLIP39 (Satoshi Labs Improvement Proposal) has to do with the Shamir Secret Sharing Scheme (SSSS). This is a way to break up any secret into N parts so that any M of the N parts can reproduce the original secret. It is not limited to, but in the context of bitcoin it is mostly used for breaking up a mnemonic sentence from BIP39 or the seed of an HD wallet and giving each piece to a different party so that reconstruction of the secret would require collaboration/collusion of at least M parties. You still get with SLIP39 a mnemonic word sentence like you do with BIP39, only the words originate from a different wordlist. So if you see a mnemonic sentence, you can lookup its words against the online published wordlists of BIP39 and SLIP39 and recognize where it comes from.
SLIP39 is actually pretty neat, in that it allows for a two-level scheme where you have group-shares and within each group you define member-shares where you define an overall group threshold and within each group a separate member threshold.
For example I can split a master secret across four groups like:
- Group-share 1:
1-of-1 for myself = single member-share and the threshold to fulfill this group-share is one i.e. I can do it by myself since I have the single member-share
- Group-share 2:
1-of-1 same as Group-share 1
- Group-share 3:
2-of-5 for my family = five member-shares (mom, dad, brother, sister, wife) and the threshold to fulfill this group-share is two i.e. any two family members together can reproduce it
- Group-share 4:
3-of-6 for friends = six member-shares (alice, bob, charlie, david, eva, frank) and the threshold to fulfill this group-share is three i.e any three of my friends together can reproduce it
And finally you set a group-threshold of two i.e. to recover the master secret the goal is to reconstruct any two of the four group-shares.
Now, to recover the master secret here are a couple of possible recovery scenarios.
Scenario 1: I can do it all by myself since I have two member-shares from two of the four group-shares (Group-1 and Group-2) that both require a single member-share.
Scenario 2: alternatively my family members and friends can come together. In particular any two family members (to fulfill Group-3) and additionally any three friends (to fulfill Group-4). This way again two (the group threshold) of the four group-shares can be fulfilled.