do european countries use the same electrical adapters?

Yes, Italy and Spain would be no issue. Only if you hop over to the UK you might need an adapter. The exception might be that it seems there is some variation in ways to ground a plug within Europe, if the plug is just a smaller two pin plug, it will be fine, if it is large and has another contact someplace on it, there could be issues with the plug fitting in some outlets.

Yes, my hair dryer had the thicker prongs and when I read the info I needed to buy a grounded adapter.

You say "do countries us the same adapter". Countries have their own plugs. No adapter needed. A two-pin plug (without ground) is call in Germany, I believe, a Formstecker. When a two-pin, ungrounded plug is used in continental Europe, it is limited by code to 2½ amps (less than 600W), which is would be a pretty anemic hair dryer. It would be illegal to sell a stronger hair dryer with a two pin plug; hair dryers in continental Europe must have grounded plugs.

A grounded plugs on a hair dryer sold in Spain would be the German Schuko type, with a cylindrical body about 1¼" in diameter with grounding clips on the side. The pins might be 4.8mm diameter, which would be too big to fit in the 4.0mm diameter holes in Italy. Even it they did fit, the grounding clips would not be connected, so what you would be doing would be technically illegal.

However, I understand that some newer constructions in Italy have a German Schuko receptacle next to a conventional Italian grounded receptacle, so then you could use the Spanish hair dryer.

As appliances with German round Schuko plugs are relatively common, it is quite easy to find adapter plugs to Italian mains.

There are also other plug designs - only in Italy there are two different types of plugs (10A and 16A), Switzerland uses his own model (three contacts arranged in triangular shape), etc.

Why do you need to buy hair dryer?

I do not recall a hotel that did not have them

If you do buy it in Spain, you probably won't need an adapter, until you get back in US.
It will come with cord that fits European plugs

peg,

This is an example of a power bar I encountered in Italy last year - https://eagle07.smugmug.com/Travel/Italy-2016/i-M3HCdKx/A .

The top outlets will accept not only the German Schuko grounded plugs but also Italian grounded plugs. The two top outlets will accept either diameter of pin on the hot and neutral pins (the center ground pin appears to accept only the smaller diameter). The side outlets will accept Italian grounded plugs or the standard two pin ungrounded Euro plugs.

I take my hairdryer from home and just use the plug adaptor mentioned above.
Works great and I have a UK adaptor for use there.
Never had a problem even in Asia, Australia, etc.
just get the appropriate adaptor and plug your hairdryer in with the caveat
mentioned above about 125/250V 60 HZ
There are several posts on this site about using our devices overseas.
I bought my set of adaptors at Wal-Mart.

Most hotels will have a decent one...the ones that are hose attached to the box are the worst....they are in Italy a lot....

I swear by this...for travel...
https://www.amazon.com/Conair-Vagabond-Compact-Folding-Handle

The cost of basic items in Europe is much higher than in the USA..if that is where you are from...VAT and just the cost of goods in general is higher...

You just need to plug...so if you go to Spain, France, and in the future Germany, UK, you use the appropriate pronged plug...if you buy a hair dryer in Spain the German or UK plug that you buy in the USA will not fit...

Duel voltage comes on most appliances these days...

I did have a hair dryer that I purchased in France and used it as I went there every 3 months or so but it died and I like this Conair better...very light weight but powerful.

Many trips to Europe and all the hotels had hair dryers in the room or you could get one from the front desk.