Do details of my undergraduate title matter? I'm a third-year undergraduate student yet to experience the graduate world.
Currently, with the course choices I made, I can choose between two degree titles, namely “BSc Mathematics” or “BSc Applied Mathematics”.

I will be taking the same courses regardless, but I'm wondering if it matters to have a different degree title.
E.g., might one of the titles benefit me or does it not matter at all (in terms of job prospects, continuing to my master’s, …)?

Moderator’s notice: Do not take this as a shopping question as to which of these specific titles is better (you can use them as examples though). Instead, focus on the relevance of such differences in the title in general.
In the long term it won't matter at all. There might be a small effect in moving to your next position depending on whether you go to grad school or to industry, but after a few years no one will notice anymore. You will be responsible for your own reputation and people will look to that, not to the specific degree you earned - especially its title. 

I also studied math, but in the US. Here we have a very broad undergraduate education, studying many things beyond the major subject. At graduation I had qualified for either a BS or a BA and was given the choice. I chose BA as it seemed to me to be more "interesting". I had taken extra courses both in math and in other subjects. But it never mattered. Literally no one cared. For entry to grad school the transcript shows what I had done. 

But, you might use the opportunity to think about what you want to do for the next ten or so years. Grad school and academia, or industry.