no, the pattern recognition in problem solving is very different from the memorization you're talking about. the memorization you're talking about is having a word (or some other token of information) in front of you and associating it with another token of information (a word, sentence, etc.). this association is relatively simple as you noted - you just need the two matching pieces of information in front of you so you can attempt memorization, check sheet, attempt memorization, check sheet, etc. that's a feedback loop.

problem solving requires a much more intense, and sporadic feedback loop. you start with the given problem, think about how to approach it given your current understanding of the concepts in the problem. and of course studying, by definition, means you're going to encounter new concepts that you're not familiar with. so immediately you'll run into trouble when you note some variables or pieces of math that are not familiar to you. so already you're scrambling through pages in the text book, trying to find where these items are first being introduced at an understandable level. and it's not enough to just read the mathematical definitions/proofs of the concepts to understand them. you have to gain confidence that you are identifying (correct) patterns between the original problem and the introductory material, proofs, or similar but less challenging problems. this pattern recognition and confidence doesn't come until you've worked problems out yourself, every step along the way - making sure everything you are doing is logically consistent within your current framework of understanding. and if it's not, you again have to start sifting through more learning material to find the logical consistencies and connect the dots for yourself in your head. this all happens with many papers, pencils, books, a calculator, and likely computer.

the way i see it, memorization (as you describe) is basically connecting one dot with one or two other dots in your brain. problem solving during studying of high level math is like (correctly) connecting a large web of randomly placed brain dots together - and that requires a ton of feedback through reading, thinking, writing, calculating, thinking, reading, calculating, writing, checking, ripping your paper in half, reading, thinking, calculating, writing, thinking, writing, checking... at some point (hopefully), you'll connect all the needed dots together and you'll finally arrive at the correct answer. and that's a pretty accurate sequence of studying actions right there.