Yes. You bring up a good analogy. Like British English compared with North American English, there are a number of words and phrases that are different, but it is still English, albeit with different accents.
Spaniards tend to be more language purists and are much more likely to cringe at a lot of the "Spanglish" ("troque" for "truck", or "lonche" for "lunch") that has crept into Mexican, TexMex and "Cali" Spanish, and to a lesser extent some parts of South America.
As far as accents go, Spaniards tend to say "th" for the "s" sound, just like Americans tend to replace "t" sounds with "d" sounds (eg, we pronounce "Patty" as Pad-ee, whereas Britons might pronounce it as Pat-tee.
However, in either case, you will be understood. It is, after all, Spanish. You just might have to ask "como?" (huh?) once a day.
I speak Spanish, and have listened to and been involved with a zillion arguments, debates and educational discussions about language differences between Hispanic countries and cultures.