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This question comes from me creating my bard character.

Under my tool proficiencies, I have "one type of musical instrument" and "any three musical instruments" does this mean I can be proficient in string instruments, and any instruments within that type, while also having proficiency with a flute, bagpipes, and drum? If this is true what are the different types of musical instruments?

"Type" is a "kind", not a "group"

From the Tools section of the Equipment chapter of the PHB (p.154):

Several of the most common types of musical instruments are shown on
the table as examples.

Table: Bagpipes Drum Dulcimer Flute Lyre [..]

Each type of musical instrument requires a separate proficiency.

From this it is clear that the PHB understands "type of musical instrument" not as a "group of musical instruments", but as a "kind of musical instrument". All such proficiencies must be taken in a given instrument and never a group of them.

You should talk to your DM about this. The rules are confusing and vague, because D&D is not usually a game where type of musical instrument matters. I don't think the designers spent much time on them. That's okay — but it generally means this isn't part of the rules-as-written which stand up to much hard thinking.

In most cases where there is cause to think about it, the DM should adjudicate either something much more relaxed than a a strict reading of the table might imply, or (in rare cases) substitute a more considered system.

In my games, I let bards be proficient in any instrument they want to be with no limits. This is because in all my years running and playing D&D, it's never mattered at all. It is entirely a bit of flavor, and if a bard can't have "I wow the locals at the tavern with whatever musical instrument is at hand" as flavor, what's the point of even being a bard? I think this is entirely appropriate in almost all games.

In fact, if a player wanted to be specially good at a particular instrument, I'd be inclined to let them have double proficiency with that one. Again, this is because I can count the number of times it would really matter in all the games I've ever played in a case other than the bard showing off their character on... zero fingers. This is right there in the same vein as "can my paladin's armor have a fancy helm which looks really cool?" or "my ranger's cat has spots".

Although it's just one "pillar" of the game, most of the mechanics of D&D focus on combat (5E, but to a large degree other editions as well). Most of the rest are to do with movement, exploration, and logistics. There's just not much in the game rules-as-written for instrument proficiency to interact with — let alone really worrying about instrument types.

There's no different die sizes, no way they might affect audiences differently, no rules about being easier to use in the middle of a battle. Nothing at all except the different prices, which are, not surprisingly, weird and arbitrary and low-design-effort. (Double-reed wind instrument? 2 gp. A stick cut into a whistle? Also 2 gp. Complicated horn with valves? Bump that up to 3 gp. Piece of goat skin stretched over a frame? 6 gp! A box with four strings on it? 25 gp, of course.) So, it really doesn't matter to the game which instrument proficiencies you have, and in most cases it's just a strange hobbling.

Of course, some games may go the other way. Musical instruments and skill with different types could be an important feature of the setting or plot. In this case, the rules need the opposite fix: house rules to provide satisfying differentiation.

You have proficiencies in four different musical instruments.

This is a case of differing language with the same meaning; in this instance, the wording used in backgrounds for proficiencies and the wording used in classes.

"One type of musical instrument" comes from your background (probably Entertainer?), where tool proficiencies that give you a choice are consistently phrased that way, at least in the Player’s Handbook (e.g. the Guild Artisan’s “one type of artisan tools”).

“Any three musical instruments" on your character sheet - or “Three musical instruments of your choice” in the class write-up - comes from your class proficiencies. This slightly different wording is used there, though as few classes grant tool proficiencies with a choice, it’s less consistent. For example, the monk has: “Choose one type of artisan’s tools or one musical instrument”.

I imagine when they added “type of” they were trying to clarify that you are proficient with all individual instruments of that type - all drums, or all harps, or all viols etc - rather than just the individual instrument you own. As mentioned in another answer, they use both terms in the Equipment chapter’s entry on musical instruments, under Tools. The instrument words chosen have varying levels of specificity though, as there are many types of drum, but a “viol” seems to mean violin, rather than all types of bowed string instrument (ie including violas, cellos and basses, assuming your campaign world has them). This is also likely intentional: what kind of musical instruments are available is probably not something most campaign worlds will specify, and it differs a lot from table to table (my current party are a band and I let them have “fantasy versions” of whatever instruments they wanted - guitars, trumpets etc - though only two of them have actual instrument proficiency).

So: if it will matter for your game, you pick a total of four instruments from the list and you have proficiency with them, allowing you to add your proficiency bonus to ability checks made to play them. (Note that when you reach second level, you will add half your proficiency bonus for all other instruments, thanks to the Jack of All Trades trait.) Talk to your DM if you’re worried about it; most won’t be hardline on this, and will generally rule that you can have your proficiency bonus on reasonably similar instruments.