Compost from your compost heap is a soil conditioner. I use it to dig into beds to improve the structure of the soil, make it more moisture retentive and add nutrients, and mulching with compost has the same effect. I dig manure in to do the same (slightly different nutrients, depending on the make up of the compost/manure).
Use potting compost to put in pots. There's soil (loam)-based potting compost, usually described as John Innes Nos 1, 2 and 3 (and seed and cutting composts). The JI refers to to the level of nutrients, 1 for pricking out seedlings and cuttings, 2 for potting on and 3 for established plants that are going to be in the pot long term. Then there's peat-based composts and peat-free composts for pots and tubs etc. Some good, some awful, some so-so.
I would always use loam-based ones if I could afford to. I use loam-based seed and cutting compost and JI No 3 for potting up large plants into pots (my fig and my apricot will go into No. 3). Apart from anything else, the added weight stops plants in pots becoming top-heavy. But for potting up my toms, pots of bedding plants etc I use 'compost' - this year I used Levington - I'd rather not use peat-based but the peat;free I tried this year was full of rubbish.
All bagged composts have fertiliser in them, and don't usually need additional fertiliser for the first couple of months after potting.
Raised beds are more or less permanent and will have plants growing in them year after year, so a mixture of topsoil and good manure is more like a permanent flower/veg bed and produces the best results.
When planting a plant or shrub out into a flower bed you are sometimes advised to dig in some compost or add some to the soil around the plant. For this I use compost from my bin if I have some, but if not some potting compost from a bag is fine.
And then of course there's specialist composts, ericaceous for lime-hating plants, cacti compost for cacti etc, etc
