I'm not diagnosed SPD, but have a lot of traits and thought I'd offer my experience.
I seem to have initiative for one thing at a time. Unfortunately, this focus can shift at a moment's notice and without warning, so I often drop whatever it is that I've been working on. I can't tell you how many obsessions I've had that have suddenly vanished. Sometimes they reappear, sometimes not.
I've been kicked out of or dropped out of school a zillion times. I finally discovered a career I wanted to pursue, and that became my focus. I actually made a longterm plan and stuck to it - got a shady job to put myself through school, got into my program, aced it, got a job right out of internship. Got licensed and moved up in my company. For the first time in my life, I had set a goal and maintained the inertia to achieve it.
But then, the boredom. Once I got to a position of leadership and essentially became the best I could be at my job, I got bored and frustrated. I could do it in my sleep now. And that made me miserable. So I had to set myself a different longterm goal, this one much (much!) more difficult. And that's what I'm doing now - working only part time so I can be back in school for the next zillion years. I could be working and making great money full-time but the lack of mental stimulation just kills me.
If I'm actively pursuing a goal, I can do all kinds of things I usually wouldn't - in trying to move up at work, I actually made a strong effort to "connect" with people and interact. I put it in quotes because it wasn't real connection - but I worked hard to perfect my act. It was successful, and I was promoted. But once I reached that position and could go no further, I stopped acting. I just can't. I surrendered that position once I started back at school, and I'm relieved that I no longer have to pretend to care about interaction - I just go in, do my job (usually with headphones on) and leave. I imagine people think something has gone wrong with me, but it doesn't bother me.
Interestingly, I seem to have more "initiative" for major goals in the long term. In my everyday life, it is sometimes impossible to get anything done because i just. don't. care. Especially if there's a social aspect. Going to the store is a serious feat.
If only I could figure out what the drive is for my longterm goals and apply that to the short term as well. I guess going to buy groceries just doesn't seem like it matters compared to working my dream job. I just wait until I am basically forced to do the mundane things - no food in the house, everything a mess, no clean clothes. Then it's like, ok ###$ it, I have to get this stuff done. I do it in a rush and feel horribly drained afterward.
As for extracurricular "fun" things or interests/hobbies.. I get ideas and feel motivated, but often don't stick to them. Lack of structure makes it difficult for me to stay focused - I think that's why I do well in school despite having to endure being around groups of people.