That Settles It 〜ようと思う

洗う becomes 洗おう, 走る becomes 走ろう, する becomes しよう, the volitional form built the same way as the plain equivalent of ましょう. と思う on top of it frames the plan as something you’ve just decided, in-the-moment, rather than a long-settled commitment.

つもり states a settled plan, often one you’ve held for a while. ようと思う leans more spontaneous, “I’ve just decided,” and ようと思っています, with ている, softens it into an ongoing intention you’ve been considering rather than a decision made on the spot.