Are these the new upcoming drive interfaces?
Yes.
So in future we should see more and more SSDs coming out with these interfaces?
Yes.
or, they just need some kind of adapters?
Yes, with caveats. M.2 SATA can be adapted to regular SATA, M.2 PCIe can be adapted to PCIe.
So SSDs will continue to be sold as SATA III, but will come with M.2 or "SATA Express" adapters.
No. If you want or need an adapter, you'll have to get one as an extra part. SATA Express will need no adapter.
The SATA Express connector is backwards-compatible with SATA. It's bulky and expensive for consumer drives, and was mainly designed to meet the needs of server backplanes, so that SATA or native PCIe drives can be chosen, with the same hardware. For you and me, it's going to be annoying.
SATA Express and NVMe (Google it) on PCIe are The Future(tm), though SATA will be allowed to die a nice slow death, like PATA before it. Also, NAND on DIMMs, but I don't know if that will ever come to consumer gear.
M.2 allows for SATA or PCIe connections, and is made as a replacement for mSATA, Mini-PCIe, 2.5" single SATA drives in any form factor (typical PCs don't have multiple drives), and custom mobile form factors. It comes in several sizes, but 2242 and 2280 seem to be the only ones anybody is using, ATM. Right now, the drives are all SATA, TMK, but a few PCIe M.2 cards are on the way (personally, I wisgood dealh M.2 lacked the SATA pins, so it could be a clean break). When M.2 native PCIe gets more popular, having a mobo with such a slot would mean you could just put the drive in and go. Since you aught to be able to get cards to adapt it when that time comes anyway, I'm not sure how worth it it is, as a value-add (OTOH, if you're a single dGPU or IGP user, and your mobo of choice happens to have one anyway, it's all good).
M.2 is set to replace 2.5" SATA and mSATA, eventually (it's already replacing mSATA quite well). If you need more drives, PCIe adapters already exist, and I'll bet you that multi-drive cards will come out, after native PCIe drives start to become popular (all they will have to do is bring pins out to a connector, and keep the signal from going to crap, once SATA becomes a, "legacy," interface).