Think of it as a sliding scale. The shinier the finish, the more light it reflects, the tougher and more wipeable it is — but the more it shows up every lump, roller mark and wonky bit of plaster underneath.
Matt is flat, almost no sheen. It's the most forgiving finish there is, which is why it's the standard for ceilings and walls. Rough plaster, filler, patches — matt hides the lot. Downside is it's harder to wipe clean, though modern washable matts have closed that gap. Farrow & Ball Estate Emulsion, Little Greene Intelligent Matt and Dulux Heritage Matt are all cracking wall finishes.
Eggshell has a low, soft sheen — the name's literal, it looks like an eggshell. This is your go-to for interior woodwork: skirting, architraves, doors, window frames. Tougher than matt, takes a wipe, but doesn't shout. Farrow & Ball Estate Eggshell and Little Greene Intelligent Eggshell are the standards here. You'll also see eggshell used on walls in high-traffic spots like hallways.
Satin sits a step shinier than eggshell. More common on metal, radiators, and in kitchens or bathrooms where you want extra wipeability. The sheen is noticeable but not mirror-like.
Gloss is the hardest, shiniest and most durable — proper old-school trim finish. It shows every imperfection mercilessly, so prep has to be spot-on, but it wears like iron and wipes clean instantly. Less fashionable than it was; most people now prefer the quieter look of eggshell on woodwork.
The "but what about" question: don't put matt on woodwork thinking it'll match your walls — it'll mark the second anyone touches it. And don't gloss a wall unless you fancy seeing every trowel mark in raking light.
Practical rule of thumb: matt on ceilings and walls, eggshell on woodwork, satin or gloss where you need maximum durability. If in doubt on trim, eggshell is the safe modern choice.