So is Italian and French. These languages all come from Latin, there called Romance Languages. The counter part for English is Germanic Languages, as in German, Dutch, Swedish, and so on. Head over to /r/linguistics for further understanding!
I'm curious what you mean by "similar linguistically"? As you already pointed out, they are both Romance languages. Do you mean that Romanian and Spanish are more similar to each other than to other Romance languages?
In what sense similar? I can read and speak Italian and Spanish fluently, and might understand some French and a good amount of Portuguese or Catalan by reading it, but Romanian seems quite different from any of those languages even when written.
While Romanian is Latin, and a Romantic language, it is an Eastern Romantic language, a different and smaller sub-branch from Western Latin (the ones Italian, Spanish, Sicilian, Catalan, Portuguese and French belong to).
Romanian and Spanish are both romantic languages, the two languages along with multiple others (french and Portuguese) all come from Latin during the rule of the Roman empire