• Basic forms
• 担ぐ — carry (on one’s shoulder) / base form
• 担ぎます — carry / masu form
• 担いだ — carried / ta form
• 担いで — carrying … / te form
• 担がない — do not carry / negative
• 担げば — if (someone) carries / conditional
• Common expressions
• みこしを担ぐ — carry a portable shrine
• 荷物を担ぐ — carry luggage (on the shoulder)

担ぐ（かつぐ） is a godan transitive verb. It often means carrying something on the shoulder, and it is common in festival contexts.

• Basic forms
• 担う — bear; shoulder (a role) / base form
• 担います — bear / masu form
• 担った — bore; took on / ta form
• 担って — bearing … / te form
• 担わない — do not bear / negative
• 担えば — if (someone) bears / conditional
• Common expressions
• 責任を担う — bear responsibility
• 未来を担う — carry the future (be responsible for the future)

担う（になう） is a godan transitive verb. It is often used in a serious / abstract sense, meaning to shoulder responsibility, roles, or the future.