If you book an itinerary in a single transaction from an online travel agency, you can be pretty sure what you get is a single (electronic) ticket issued by one of the airlines in question (the plating carrier). You pay the travel agency, who pays the plating carrier, who pays the other airlines in the itinerary.
On sites such as this one, you will often meet the question "is it all on one ticket?" This is not because you risk getting your itinerary split into several tickets in an ordinary booking. Rather, the question is asked to exclude corner cases where you've been talking to an actual human travel agent and they decide to split the booking into multiple ones in order to finagle together the itinerary you want (which the automated systems would simply refuse to do in one go) or get special deals for you -- or of course if you piece it together from multiple bookings yourself.
So when you're making a single booking you can be sure you're covered for onward transportation in case of missed connections.
Note that this does not necessarily mean that you have a single PNR locator. It may need to be different if different legs on your itinerary are flown by airlines that use different GDS providers to manage their reservations.
However, what you're asking for is getting baggage checked through -- and in that case it is not actually the PNR that governs, but instead these two questions:
- Are all legs on the same ticket? (That means, the same e-ticket number).
- Do the airlines in question transfer baggage at all in each of your layover points?
Booking everything in one go should make you pretty sure that the answer to the first question is "yes".
The second question is harder and depends on the airlines and airports. In general you ought to feel safe if (a) both airlines are full-service airlines, (b) the airport is a hub for at least one of the airlines, and (c) they interline well enough that you can book the connection there in the first place.
If neither airline has a hub at the connection point (but they are still full-service), there's still a good chance that your baggage can be transferred if it is still a hub for someone that the two airlines interline with.
On the other hand, if you're making a rare connection at a smallish airport where it is unusual for anyone to connect, it may be that it's simply impossible: The ground operations is not set up to take bags from arriving planes anywhere else than to a baggage carousel where you need to pick it up.
In the two latter cases, my recommendation is to contact one of the airlines before booking and ask if they interline baggage at XYZ with other airline such-and-such.
A final wrinkle is that even if you can get your bags checked through it may not be possible to issue a boarding card for all your legs at the airport you start out at. This is getting rarer nowadays -- and can be moot if the second airline lets you check in and get a boarding pass online -- but in some cases you may still need to go to the (airside) transfer desk at the layover point to get your onward boarding pass printed. You won't need to worry about in advance anyway, though.
(Why, then, is the standard question "do you have a single PNR", rather than "do you have a single e-ticket number", when it's the latter that matters? Mostly because it's easier for most people to find and compare the PNR in the paperwork they get from their travel agent, than to look for an e-ticket number somewhere in the small print. If the PNRs do match, then it's certain that there's also a single underlying ticket; if they're different more investigation may be needed.)
In your particular case: SilkAir is a regional subsidiary of Singapore Airlines, who is in Star Alliance together with Lufthansa. Even though SilkAir is not itself a Star Alliance member, you can rest assured that they interline baggage with their parent's alliance partners at their own main hub.
