I've not got just one, but two of them, Eulalia!
Like you I pondered the 'is he active or hyperactive' question at length, especailly with son number one, since I had never had a toddler before. I decided active was more appropriate. I kept asking teachers and nursery workers this question too. It's good to get a variety of opinions, especially from those who see your child in a group situation away from you, I think. All the people I asked said 'active' for bot son number on and son number two. Partly this is on account of the hours my sons sleep. Even if the youngest is not such a good sleeper, he still clocks up the hours - about 11 a night. (Quick update, he does have to odd half hour to an hour daytime nap, but his bedtime is now mostly before 8.30 - he settles much better, than a year ago and even asks to be put to bed. I think nursery days are the reason for this change as I said on another thread).
Anyway, as I understand it, a hyperactive child really is awake for lots more hours. That's not to say my active boys are problem free. My oldest son's behaviour has always been an issue at school. My youngest son distinguished himself by flinging a changing mat at the assessor,and throwing a wobbly after he sucessfully completed his three and a half year assessment recently. The assesor would not let him climb on the table in the consulting room and he became very cross. She was not impressed and did not look like she believed me when I said this type of outburst was not a common thing. The upshot is that we've got to have another test. Anyway, enough of my problems for now.
Eulalia, one thing that is different between my two sons age 3/4 is this: the oldest was so attention demanding. There was no chance of me reading even two paragraphs of a paper when we were together indoors. My youngest is more self reliant. I can browse the sunday papers while he watches a video, he will sit through a whole disney film at the cimema, he will run off and play happily with other children when we go to a play centre. My oldest insisted I followed him through all the tunnels and made me sit with him wheil he watched TV. I found it much more draining looking after my oldest even though he slept through 12 hours at night. He ran around a lot but it was not just this. He just wanted tons of attention from me or indeed any adult carer all the time. Teachers found the same thing when he started school.
I think it's easy to mix up the effect a child is having on you with the way a child is. My oldest son's personality drove me to distraction sometimes. I'm not saying this is what is happening with you, but I htink in myu case it colourd my feelings towards his activeness. Funnily enough,the 3 year assessors were much more positive about my oldest son, while I felt quite negative. Yet with my youngest son, the assessor was for more negative than me! I don't find my youngest son's behaviour a huge problem, would say he is a better behaved three year old than his older brother was. He is sociable, not a hitter, shares OK etc etc. Yet the nursery want him ( and several others in his class) to be looked at by an SEN advisor as a precaution and to suggest ways of controlling them. And this assessor wants to do another assessment at our home.
Anyway, going back to your question on does it get better and what should you expect at this age, I think your son is just at a very active age. I'm not sure how much he will calm down naturally in the next six mohts or so. I don't think my oldest did, though his attention span did begin to increase. However, both my sons got tired more easily at home in the evening once they had a full day at nursery (ie 5 or 6 hours). It was the new environment, new routines and most of all, I think, the new people. If there is any way you can arrage for your son to have longer nursery days (if he's happy to have them of course) I'd go for it. If this is not possible, I'm sure you'll find that when your son starts school he will seem mre tired in the evenings and ready for bed at a 'normal' time.
I am in a rush, so will end now, but will post more if I think of anything.