Putting different lead acid batteries in parallel can be OK. It is sometimes done on vehicles for example so a caravan can have an "auxiliary" battery that is independent of the vehicle's battery. This is to ensure if the auxiliary battery is depleted, the vehicle's isn't. See this link for more information on that.
In practice, all sorts of nasty things are done to batteries. It is a sliding scale between shortening the life of the batteries, and shortening the life of the person using them.
Lead acid batteries have incredibly complex personalities, which even vary between identical batteries from the same batch.
There are different families of lead acid batteries, such as AGM, SLI, calcium, VRLA, SLA.
The car battery is most likely an SLI or SLI calcium battery. The one in the photo is some form of SLA.
They are probably similar enough to work together, but be careful when first putting them in parallel - try to get them to be at the same voltage first, without over-straining the 15Ah battery. (But to answer your question, it is by definition that when in parallel, they will always have the same voltage. Sparks and death of battery and/or user may occur.)
As for charging them, they can not be charged in the same way as a car battery because the SLA, a sealed lead acid battery, cannot freely gas while being over-charged. See this link for more info. I believe you would need to charge the pair as if they were both sealed lead acid batteries, but this may or may not be appropriate or possible for the use you were intending for them.
However when you do get them working together, the car battery's capacity will probably be essentially increased. But by how much is debatable and depends on an awful lot, including how they are charged and discharged.
But if you are trying to save money and just use what you have, I would argue that this is not the way to go as you will probably decrease the life of one or both batteries. And if you are not trying to save money, in reality I would suggest make your life easier and perhaps get a second car battery instead of the SLA.