The big, fuzzy ping pong ones are usually Buff Tailed or White Tailed Bumblebee Queens.
If they're up high, they're after nectar from tree blossom, but if they're flying low, they're probably 'quartering' which means looking for a suitable spot to start this year's colony. Dandelions are probably the most important food source (they have nectar for energy and pollen is their protein source) for emerging Queens and the first brood.
Hibernation sites include plant pots and, very specifically, under sheds in old mouse nests.
A bumble colony is around 20-200 bees on average, compared to a honeybee colony of 50,000 odd in midsummer - all but the newly fertilised Queens will die in Autumn, which is why they aren't 'aggressive' - they aren't protecting a massive stock of food for tens of thousands through winter, there's just a tiny honeypot for summer food.
Tiny dark bumbles about the size of your little fingernail are Tree Bumblebees. They're a blow in over the last few years from France but don't have a negative effect upon native ones in the slightest. If you have bumbles living in a bird nesting box, in a compost heap or in a tree (the clue's in the name there), it's going to be Tree Bumbles. They're also quite fond of chimneypots and no absolutely zero damage to either human or house.
Bumbles as a whole pollinate far more species of plant than honeybees because they vary so much in size and shape of or body, face and tongue.
Some have evolved to rob long, narrow flowers of nectar that they can't get into normally by nipping little holes at the base - nectar robbing. And buzz pollination is remarkable - you often hear it around tomato flowers; bumbles hold the flower and vibrate their wings at a frequency that causes the flower to drop pollen. Interestingly enough, it's at a frequency around middle g# for many flowers.
Mason bees don't harm masonry at all, they move stuff (eg, grains of mortar) that's already loose. Builders like saying it'll cost thousands because then they make thousands.
There are also solitary bees that fulfil yet another evolutionary niche. Whilst they are solitary in that they don't form a colony, they do have identical likes amongst their species, which is how you get grass banks over sand that are full of them. They don't sting. Leafcutter bees look amazing and also love using rose petals to make the wraps for their eggs.
There are some flies that mimic bumblebees because they parasitise Bumblebee nests by flicking their eggs in from a distance. Logically enough, they're called Bee Flies.
The Bumblebee Conservation Trust is a great resource and has ID charts of many common bumbles. Before Covid, they did workshops on identifying Bumbles and their habits - if they've started them again, it'll be around now to take advantage of seeing the queens out and about quartering.
They need water - marbles in a dish make it safe for them - and sugar water is the safe way to help a cold and tired bumble, such as one you find in the house of a morning. If they're outside, try and get them onto a patch where there's sunshine. The bigger the bumble, the later it wants to get up in the morning because of the need for warmth - the Early Bee gets its name because it can function in cooler temperatures early in the morning and season.
Other than that, don't kill them, don't use bug spray/insecticides in the garden - ever - they won't hurt you unless you are literally about to squash them - and grow things like Lavender, Daisies, Dandelions, Foxgloves, Borage, and Nasturtiums. Be careful off 'bee friendly' plants in garden centres because they've often been treated with insecticides in the nurseries which then kill the bees they're being sold to help.
Oh, and bumbles are an absolutely vital food source for blue tits as their broods hatch in Spring. That's how you can find a mound of hollowed out bumbles underneath a flowering cherry tree.